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BEGIN:VEVENT
SUMMARY:Georgios Dosidis (University of Missouri\, Columbia)
DTSTART:20201008T134000Z
DTEND:20201008T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/1/">Linear and multilinear spherical maximal functions</a>\nby Georgios
  Dosidis (University of Missouri\, Columbia) as part of Function spaces\n\
 n\nAbstract\nThe classical spherical maximal function is an analogue of th
 e Hardy-Littlewood maximal function that involves averages over spheres in
 stead of balls. We will review the classical bounds for the spherical maxi
 mal function obtained by Stein and explore their implications for partial 
 differential equations and geometric measure theory. The main focus of thi
 s talk is to discuss recent results on the multilinear spherical maximal f
 unction and on a family of operators between the Hardy-Littlewood and the 
 spherical maximal function. We will cover boundedness and convergence resu
 lts for these operators for the optimal range of exponents. We will also i
 nclude a discussion on Nikodym-type sets for spheres and spherical maximal
  translations.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Breit (Heriot-Watt University\, Edinburgh)
DTSTART:20201022T134000Z
DTEND:20201022T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/2/">Optimal Sobolev embeddings for symmetric gradients (joint work with
  Andrea Cianchi)</a>\nby Dominic Breit (Heriot-Watt University\, Edinburgh
 ) as part of Function spaces\n\n\nAbstract\nI will present an unified appr
 oach to embedding theorems for Sobolev type spaces of vector-valued functi
 ons\, defined via their symmetric gradient. The Sobolev spaces in question
  are built upon general rearrangement-invariant norms. Optimal target spac
 es in the relevant embeddings are determined within the class of all rearr
 angement-invariant spaces. In particular\, I show that all symmetric gradi
 ent Sobolev embeddings into rearrangement-invariant target spaces are equi
 valent to the corresponding embeddings for the full gradient built upon th
 e same spaces.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Cruz-Uribe\, OFS (University of Alabama\, Tuscaloosa)
DTSTART:20201015T134000Z
DTEND:20201015T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/3/">Norm inequalities for linear and multilinear singular integrals on 
 weighted and variable exponent Hardy spaces</a>\nby David Cruz-Uribe\, OFS
  (University of Alabama\, Tuscaloosa) as part of Function spaces\n\n\nAbst
 ract\nI will discuss recent work with Kabe Moen and Hanh Nguyen on norm in
 equalities of the form\n$$T\\colon H^{p_1}(w_1)\\times H^{p_2}(w_2)\\to L^
 p(w)\,$$\nwhere $T$ is a bilinear Calderón-Zygmund singular integral oper
 ator\, $0 < p\, p_1\, p_2 <\\infty$ and\n$$\\frac1{p_1} + \\frac1{p_2} = \
 \frac1p\,$$\nthe weights $w\, w_1\, w_2$ are Muckenhoupt weights\, and the
  spaces $H^{p_i}(w_i)$ are the weighted Hardy spaces introduced by Strombe
 rg and Torchinsky.\nWe also consider norm inequalities of the form\n$$T\\c
 olon H^{p_1(\\cdot)} \\times H^{p_2(\\cdot)} \\to L^{p(\\cdot)}\,$$\nwhere
  $L^{p(\\cdot)}$ is a variable Lebesgue space (intuitively\, a classical L
 ebesgue space with the constant exponent p replaced by an exponent functio
 n $p(\\cdot)$) and the spaces $H^{p_i(\\cdot)}$ are the corresponding vari
 able exponent Hardy spaces\, introduced by me and Li-An Wang and independe
 ntly by Nakai and Sawano.\nTo illustrate our approach we will consider the
  special case of linear singular integrals. Our proofs\, which are simpler
  than existing proofs\, rely heavily on three things: finite atomic decomp
 ositions\, vector-valued inequalities\, and the theory of Rubio de Francia
  extrapolation.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Lesnik (Poznan University of Technology)
DTSTART:20201029T144000Z
DTEND:20201029T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/4/">Factorization of function spaces and pointwise multipliers</a>\nby 
 Karol Lesnik (Poznan University of Technology) as part of Function spaces\
 n\n\nAbstract\nGiven two function spaces $X$ and $Y$ (over the same measur
 e space)\, we say that $X$ factorizes $Y$ if  each $f\\in Y$ may be writte
 n as a product \n\\[\nf=gh \\ \\ {\\rm \\ for\\ some\\ } g\\in X {\\rm \\ 
 and\\ } h\\in M(X\,Y)\,\n\\]\nwhere $M(X\,Y)$ is the space of pointwise mu
 ltipliers from $X$ to $Y$. \n\nDuring the lecture I will present recent de
 velopments in the subject of factorization. The problem whether one space 
 may be factorized by another will be discussed for general function lattic
 es as well as  for special classes of function spaces. \nMoreover\, it wil
 l be explained why the developed methods may be regarded as a kind of arit
 hmetic of function spaces.  Finally\, the problem of regularizations for f
 actorization will be presented together with a number of applications.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irshaad Ahmed (Sukkur IBA University)
DTSTART:20201105T144000Z
DTEND:20201105T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/5/">On Limiting Approximation Spaces with Slowly Varying Functions</a>\
 nby Irshaad Ahmed (Sukkur IBA University) as part of Function spaces\n\n\n
 Abstract\nThis talk is concerned with limiting approximation spaces involv
 ing slowly varying functions\, for which we establish some interpolation f
 ormulae via limiting reiteration. An application to Besov spaces is given.
 \n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gord Sinnamon (University of Western Ontario\, London)
DTSTART:20201112T144000Z
DTEND:20201112T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/6/">A Normal Form for Hardy Inequalities</a>\nby Gord Sinnamon (Univers
 ity of Western Ontario\, London) as part of Function spaces\n\n\nAbstract\
 nLet $b$ be a non-negative\, non-increasing function on $(0\,\\infty)$ and
  let $H_bf(x) =\\int_0^{b(x)}f$. The inequality $\\|H_bf\\|q\\le C\\|f\\|_
 p$ expresses the boundedness of this operator from unweighted $L^p(0\,\\in
 fty)$ to unweighted $L^q(0\,\\infty)$. It is called a <i>normal form Hardy
  inequality</i>.\n \nAn abstract formulation of a Hardy inequalities is gi
 ven and every abstract Hardy inequality is shown to be equivalent\, in a s
 trong sense\, to one in normal form. This equivalence applies to Hardy ope
 rators and their duals of the weighted continuous\, weighted discrete\, an
 d general measures types\, as well as those based on averages over starsha
 ped sets in many dimensions. A straightforward formula relates each Hardy 
 inequality to its normal form parameter $b$.\n \nBesides giving a uniform 
 treatment of many different types of Hardy operator\, the reduction to nor
 mal form provides new insights\, simple proofs of known theorems\, and new
  results concerning best constants.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Cianchi (University of Florence)
DTSTART:20210107T140000Z
DTEND:20210107T150000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/7/">Optimal embeddings for fractional-order Orlicz-Sobolev spaces</a>\n
 by Andrea Cianchi (University of Florence) as part of Function spaces\n\n\
 nAbstract\nThe optimal Orlicz target space is exhibited for embeddings of 
 fractional-order Orlicz-Sobolev spaces in the Euclidean space. An improved
  embedding with an Orlicz-Lorentz target space\, which is optimal in the b
 roader class of all rearrangement-invariant spaces\, is also established. 
 Both spaces of order less than one\, and higher-order spaces are considere
 d. Related Hardy type inequalities are proposed as well. This is a joint w
 ork with A. Alberico\, L. Pick and L. Slavíková.\n\nPlease be aware that
  this seminar starts at an unusual time (40 mins earlier).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Diening (Bielefeld University)
DTSTART:20201119T144000Z
DTEND:20201119T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/8/">Elliptic Equations with Degenerate Weights</a>\nby Lars Diening (Bi
 elefeld University) as part of Function spaces\n\n\nAbstract\nWe study the
  regularity of the weighted Laplacian and $p$-Laplacian with\ndegenerate e
 lliptic matrix-valued weights.  We establish a novel\nlogarithmic BMO-cond
 ition on the weight that allows to transfer higher\nintegrability of the d
 ata to the gradient of the solution. The\nsharpness of our estimates is pr
 oved by examples.\n\nThe talk is based on joint work with Anna Balci\, Raf
 faella Giova and\nAntonia Passarelli di Napoli.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Lang (The Ohio State University)
DTSTART:20201126T144000Z
DTEND:20201126T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/9/">Extremal functions for Sobolev Embedding and non-linear problems</a
 >\nby Jan Lang (The Ohio State University) as part of Function spaces\n\n\
 nAbstract\nWe will focus on extremal functions for Sobolev Embbedings of f
 irst and second order and at the eigenfunctions and eigenvalues of corresp
 onding non-linear problems (i.e. $pq$-Laplacian and $pq$-bi-Laplacian on i
 nterval or rectangular domain). The main results will be the full characte
 rization of spectrum for corresponding non-linear problems\, geometrical p
 roperties of eigenfunctions and their connection with Approximation theory
 .\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Kalamajska (University of Warsaw)
DTSTART:20201203T144000Z
DTEND:20201203T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/10/">Strongly nonlinear multiplicative inequalities</a>\nby Agnieszka K
 alamajska (University of Warsaw) as part of Function spaces\n\n\nAbstract\
 nIn 2012  together with Jan Peszek we obtained the following inequality:\n
 $$\n  \\int_{(a\,b)} |f^{'}(x)|^qh(f(x))dx \\le\n   C \\int_{(a\,b)}\n    
 \\left( \\sqrt{|f^{''}(x){\\mathcal T}_{h}(f(x))| }\\right)^qh(f(x))dx\,\n
 \\tag{1}\n$$\n  as well as  its Orlicz  variants\,\n  where ${\\mathcal T}
 _{h}(\\cdot)$ is certain transformation of function  $f$ with the property
  ${\\mathcal T}_{\\lambda^\\alpha}(f)\\sim f$\, generalizing previous resu
 lts in this direction due to Mazja.\n\nInequalities in the form (1) were f
 urther generalized  in several directions in the chain of my joint works  
 with Katarzyna Pietruska-Paluba\, Jan Peszek\, Katarzyna Mazowiecka\, Toma
 sz Choczewski\, Ignacy Lipka and with Alberto Fiorenza and  Claudia Capogn
 e\, Tomáš Roskovec and Dalmil Peša.\n\n I will discuss various versions
  of inequality (1)\, together with its multidimensional variants.\n We wil
 l also show some applications of such inequalities to the regularity theor
 y for degenerated PDE’s of elliptic type.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Molchanova (University of Vienna)
DTSTART:20201217T144000Z
DTEND:20201217T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/11/">An extended variational approach for nonlinear PDE via modular spa
 ces</a>\nby Anastasia Molchanova (University of Vienna) as part of Functio
 n spaces\n\n\nAbstract\nLet $H$ be a Hilbert space and $\\varphi\\colon H 
 \\to [0\,\\infty]$ be a convex\, lower-semicontinuous\, and proper modular
 .\nWe study an evolution equation\n$$\n  \\partial_t u + \\partial \\varph
 i (u) \\ni f\, \\qquad u(0)=u_0\n\\tag{1}\n$$\nfor $t\\in[0\,T]$ and $f\\i
 n L^1(0\,T\;H)$.\nIf $u_0\\in H$ and $\\partial \\varphi$ is considered as
  a nonlinear operator from $V$ to $V^*$\, for some separable and reflexive
  $V\\subset H$\,\none can apply the classical variational approach to obta
 in well-posedness of problem (1).\nIn this talk\, we present a more genera
 l method\, which allows to treat (1) in nonseparable or nonreflexive cases
  of modular spaces $L_{\\varphi}$ instead of $V$.\n\nThis is a joint work 
 with A. Menovschikov and L. Scarpa.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Alberico (Italian National Research Council\, Naples)
DTSTART:20210114T144000Z
DTEND:20210114T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/12/">Limits of fractional Orlicz-Sobolev spaces</a>\nby Angela Alberico
  (Italian National Research Council\, Naples) as part of Function spaces\n
 \n\nAbstract\nWe establish versions for fractional Orlicz-Sobolev seminorm
 s\, built upon Young functions\, of the Bourgain-Brezis-Mironescu theorem 
 on the limit as $s\\to 1^-$\, and of the Maz’ya-Shaposhnikova theorem on
  the limit as $s\\to 0^+$\, dealing with classical fractional Sobolev spac
 es. As regards the limit as $s\\to 1^-$\, Young functions with an asymptot
 ic linear growth are also considered in connection with the space of funct
 ions of bounded variation. Concerning the limit as $s\\to 0^+$\, Young fun
 ctions fulfilling the $\\Delta_2$-condition are admissible. Indeed\, count
 erexamples show that our result may fail if this condition is dropped. Thi
 s is a joint work with Andrea Cianchi\, Luboš Pick and Lenka Slavíková.
 \n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Evseev (Steklov Mathematical Institute\, Moscow)
DTSTART:20210121T144000Z
DTEND:20210121T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/13/">Vector-valued Sobolev spaces based on Banach function spaces</a>\n
 by Nikita Evseev (Steklov Mathematical Institute\, Moscow) as part of Func
 tion spaces\n\n\nAbstract\nIt is known that for Banach valued functions th
 ere are several approaches to define a Sobolev class. We compare the usual
  definition via weak derivatives with the Reshetnyak-Sobolev space and wit
 h the Newtonian space\; in particular\, we provide sucient conditions whe
 n all three agree. As well we revise the difference quotient criterion and
  the property of Lipschitz mapping to preserve Sobolev space when it actin
 g as a superposition operator.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Winfried Sickel (Friedrich Schiller University\, Jena)
DTSTART:20210128T144000Z
DTEND:20210128T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/14/">Complex Interpolation of Smoothness Spaces built on Morrey Spaces<
 /a>\nby Winfried Sickel (Friedrich Schiller University\, Jena) as part of 
 Function spaces\n\n\nAbstract\nLet  $\\mathcal{M}_p^u([0\,1]^d)$ denote th
 e Morrey space on the cube $[0\,1]^d$ and $[\\\, \\cdot\\\, \, \\\, \\cdot
 \\\,]_\\Theta$\, $0 < \\Theta <1 $\, \nrefers to the complex method of int
 erpolation. We shall discuss generalizations of the formula \n\\[\n\\left[
 \\mathcal{M}^{u_0}_{p_0}([0\,1]^d)\,\\\,\\mathcal{M}^{u_1}_{p_1}([0\,1]^d)
 \\right]_\\Theta = \\overset{\\diamond}{\\mathcal{M}_p^u}([0\,1]^d)\\\, \,
 \n\\]\nif\n\\[\n1\\le p_0 < u_0 <\\infty\, \\quad 1 < p_1< u_1 <\\infty\, 
 \\quad p_0 < p_1\,\n\\quad 0 < \\Theta < 1\n\\]\nand\n\\[\np_0\\\, \\cdot\
 \\,  u_1 = p_1\\\, \\cdot \\\,  u_0\\\, \, \\quad\n\\frac1p:=\\frac{1-\\Th
 eta}{p_0}+\\frac{\\Theta}{p_1}\\\, \, \\quad\n\\frac1u:=\\frac{1-\\Theta}{
 u_0}+\\frac{\\Theta}{u_1}\\\, .\n\\]\nFor a domain $ \\Omega \\subset \\ma
 thbb{R}^d$ the space $\\overset{\\diamond}{\\mathcal{M}_p^u}(\\Omega)$ is 
 defined as the closure of the smooth \nfunctions with respect to the norm 
 of the space $\\mathcal{M}_p^u(\\Omega)$.\nThe generalizations will includ
 e more general bounded domains (Lipschitz domains) and more general functi
 on spaces\n(Lizorkin-Triebel-Morrey spaces). \n\n \nMy talk will be based 
 on joint work with Marc Hovemann (Jena) and \nCiqiang Zhuo (Changsha).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Behnam Esmayli (University of Pittsburgh)
DTSTART:20201210T144000Z
DTEND:20201210T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/15/">Co-area formula for maps into metric spaces</a>\nby Behnam Esmayli
  (University of Pittsburgh) as part of Function spaces\n\n\nAbstract\nCo-a
 rea formula for maps between Euclidean spaces contains\, as its very speci
 al cases\, both Fubini's theorem and integration in polar coordinates form
 ula.\n          In 2009\, L. Reichel proved the coarea formula for maps fr
 om Euclidean spaces to general metric spaces. I will discuss a new proof o
 f the latter by the way of an implicit function theorem for such maps.\n  
         An important tool is an improved version of the coarea inequality 
 (a.k.a Eilenberg inequality) that was the subject of a recent joint work w
 ith Piotr Hajlasz.\n          Our proof of the coarea formula does not use
  the Euclidean version of it and can thus be viewed as new (and arguably m
 ore geometric) in that case as well.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Pérez (Basque Center for Applied Mathematics)
DTSTART:20210204T144000Z
DTEND:20210204T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/16/">Fractional Poincaré inequalities and Harmonic Analysis</a>\nby Ca
 rlos Pérez (Basque Center for Applied Mathematics) as part of Function sp
 aces\n\n\nAbstract\nIn this mostly  expository lecture\,  we will discuss 
 some recent results concerning fractional Poincaré and Poincaré-Sobolev 
 inequalities with weights\, the degeneracy. These results improve some wel
 l known estimates due to Fabes-Kenig-Serapioni  from the 80's in connectio
 n with the local regularity of solutions of  degenerate elliptic equations
  and also some more recent results by\nBourgain-Brezis-Minorescu.  Our app
 roach is different from the usual ones and it is based on methods that com
 e from Harmonic Analysis\, in particular there is intimate connection with
  the BMO spaces.\nIf we have time we  will discuss also some new results i
 n the context of multiparameter setting improving also some results from S
 hi-Torchinsky and\nLu-Wheeden from the 90's.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Carro (Universidad Complutense de Madrid)
DTSTART:20210218T144000Z
DTEND:20210218T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/17/">Boundedness of Bochner-Riesz operators on rearrangement invariant 
 spaces</a>\nby María Carro (Universidad Complutense de Madrid) as part of
  Function spaces\n\n\nAbstract\nWe shall present very briefly the Bochner-
 Riesz conjecture\, which is an open problem in dimension $n > 2$\, and we 
 shall prove\, with the help of the extrapolation theory of Rubio de Franci
 a\, some estimates for the decreasing rearrangement of $B_\\alphaf$\, wher
 e $B_\\alpha$ is the B-R operator.\n\nAs a consequence\, we can give suffi
 cient conditions (which are necessary sometimes) for the boundedness of $B
 _\\alpha$ in weighted Lorentz spaces among other rearrangement invariant s
 paces. \n\nThis is a joint work with Jorge Antezana\, Elona Agora and my P
 hD student Sergi Baena.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Soria (Universidad Complutense de Madrid)
DTSTART:20210225T144000Z
DTEND:20210225T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/18/">Optimal doubling measures and applications to graphs</a>\nby Javie
 r Soria (Universidad Complutense de Madrid) as part of Function spaces\n\n
 \nAbstract\nIn a joint work with P. Tradacete\, we have recently proved th
 at the doubling constant on any homogeneous metric measure space is at lea
 st 2. Continuing with this line of research\, and in collaboration with E.
  Durand-Cartagena\, we have studied further results in the discrete case o
 f graphs\, showing the connection between the optimal constant and spectra
 l properties.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kristensen (University of Oxford)
DTSTART:20210304T144000Z
DTEND:20210304T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/19/">Regularity and uniqueness results in some variational problems</a>
 \nby Jan Kristensen (University of Oxford) as part of Function spaces\n\n\
 nAbstract\nIt is known that minimizers of strongly polyconvex variational 
 integrals need not be regular nor unique. However\, if a suitable Gårding
  type inequality is assumed for the variational integral\, then both regul
 arity and uniqueness of minimizers can be restored under natural smallness
  conditions on the data. In turn\, the Gårding inequality turns out to al
 ways hold under an a priori C1 regularity hypothesis on the minimizer\, wh
 ile its validity is not known in the general case. In this talk\, we discu
 ss these issues and how they are naturally connected to convexity of the v
 ariational integral on the underlying Dirichlet classes.\n\nPart of the ta
 lk is based on ongoing joint work with Judith Campos Cordero\, Bernd Kirch
 heim and Jan Kolář\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nenad Teofanov (University of Novi Sad)
DTSTART:20210211T144000Z
DTEND:20210211T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/20/">Continuity properties of analytic pseudodifferential operators</a>
 \nby Nenad Teofanov (University of Novi Sad) as part of Function spaces\n\
 n\nAbstract\nMotivated by some questions in quantum mechanics\, V. Bargman
 n (in 1960s) introduced and studied integral transform that now bears his 
 name. More recently\, J. Toft studied the mapping properties of the Bargma
 nn transform when acting on Feichtinger’s modulation spaces. These inves
 tigations served as a starting point in the recent study of analytic pseud
 odifferential operators. Our aim is to give an introduction to recent resu
 lts in that direction\, obtained with J. Toft and P. Wahlberg.\nIn the fir
 st part of the talk\, we provide a historical background by discussing Her
 mite functions\, linear harmonic oscillator\, and different spaces of (ult
 ra)differentiable functions\, notably Pilipovic spaces. Thereafter\, we in
 troduce the Bargmann transform and analytic pseudodifferential operators. 
 To stress the connection with the classical theory\, we will consider Wick
  and anti-Wick connection. At the end\, we briefly mention how our finding
 s can be used to recover and improve some known results in the context of 
 real analysis.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Kaltenbach (University of Freiburg)
DTSTART:20210311T144000Z
DTEND:20210311T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/21/">Variable exponent Bochner–Lebesgue spaces with symmetric gradien
 t structure</a>\nby Alex Kaltenbach (University of Freiburg) as part of Fu
 nction spaces\n\n\nAbstract\nWe introduce function spaces for the treatmen
 t of non-linear parabolic equations with variable log-Hölder continuous e
 xponents\, which only incorporate information of the symmetric part of a g
 radient. As an analogue of Korn’s inequality for these functions spaces 
 is not available\, the construction of an appropriate smoothing method pro
 ves itself to be difficult. To this end\, we prove a point-wise Poincaré 
 inequality near the boundary of a bounded Lipschitz domain involving only 
 the symmetric gradient. Using this inequality\, we construct a smoothing o
 perator with convenient properties. In particular\, this smoothing operato
 r leads to several density results\, and therefore to a generalized formul
 a of integration by parts with respect to time. Using this formula and the
  theory of maximal monotone operators\, we prove an abstract existence res
 ult.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Cobos (Universidad Complutense de Madrid)
DTSTART:20210415T134000Z
DTEND:20210415T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/22/">Interpolation of compact bilinear operators</a>\nby Fernando Cobos
  (Universidad Complutense de Madrid) as part of Function spaces\n\n\nAbstr
 act\nInterpolation of compact bilinear operators is a problem already cons
 idered by Calderón [2] in his foundational paper on the complex interpola
 tion method. The study on the real method started more recently with the p
 apers by Fernadez and Silva [6] and Fernández-Cabrera and Martínez [7\, 
 8]. An important motivation for this research has been the fact that compa
 ct bilinear operators occur rather naturally in harmonic analysis (see\, f
 or example\, the paper by Bényi and Torres [1]).\n\nIn this talk\, we wil
 l review some recent results on the topic taken from joint papers with Fer
 nández-Cabrera and Martínez [3\, 4\, 5].\n\n\n$\\text{\\large References
 }$\n\n$\\text{\n[1] Á.Bényi and R.H.Torres\, \\textit{Compact bilinear o
 perators and commutator}\, Proc. Amer. Math. Soc. 141 (2013) 3609–3621.\
 n}$\n$\\text{\n[2] A.P. Calderón\, \\textit{Intermediate spaces and inter
 polation\, the complex method}\, Studia Math. 24 (1964) 113–190.\n}$\n$\
 \text{\n[3] F. Cobos\, L.M. Fernández-Cabrera and A. Martínez\, \\textit
 {Interpolation of compact bilinear operators among quasi-Banach spaces and
  applications}\, Math. Nachr. 291 (2018) 2168–2187.\n}$\n$\\text{\n[4] F
 . Cobos\, L.M. Fernández-Cabrera and A. Martínez\, \\textit{On compactne
 ss results of Lions-Peetre type for bilinear operators}\, Nonlinear Anal. 
 199 (2020) 111951.\n}$\n$\\text{\n[5] F. Cobos\, L.M. Fernández-Cabrera a
 nd A. Martínez\, \\textit{A compactness result of Janson type for bilinea
 r operators}\, J. Math. Anal. Appl. 495 (2021) 124760.\n}$\n$\\text{\n[6] 
 D.L. Fernandez and E.B. da Silva\, \\textit{Interpolation of bilinear oper
 ators and compactness}\, Nonlinear Anal. 73 (2010) 526–537.\n}$\n$\\text
 {\n[7] L.M. Fernández-Cabrera and A. Martínez\, \\textit{On interpolatio
 n properties of compact bilinear operators}\, Math. Nachr. 290 (2017) 1663
 –1677.\n}$\n$\\text{\n[8] L.M. Fernández-Cabrera and A. Martínez\, \\t
 extit{Real interpolation of compact bilinear operators}\, J. Fourier Anal.
  Appl. 24 (2018) 1181–1203.\n}$\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans G. Feichtinger (TU Wien and NuHAG)
DTSTART:20210318T144000Z
DTEND:20210318T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/23/">Completeness of sets of shifts in invariant Banach spaces of funct
 ions</a>\nby Hans G. Feichtinger (TU Wien and NuHAG) as part of Function s
 paces\n\n\nAbstract\nWe show that well-established methods from the theory
  of Banach modules and time-frequency analysis allow to derive completenes
 s results for the collection of shifted and dilated version of a given (te
 st) function in a quite general setting. While the basic ideas show strong
  similarity to the arguments used in a recent paper by V. Katsnelson we ex
 tend his results in several directions\, both relaxing the assumptions and
  widening the range of applications. There is no need for the Banach space
 s considered to be embedded into $(L^2(\\mathbb R)\, \\|\\cdot\\|_2)$\, no
 r is the Hilbert space structure relevant. We choose to present the result
 s in the setting of the Euclidean spaces\, because then the Schwartz space
  $\\mathcal S'(\\mathbb R^d)$ $(d \\ge 1)$ of tempered distributions provi
 des a well-established environment for mathematical analysis. We also esta
 blish connections to modulation spaces and Shubin classes $(Q_s(\\mathbb R
 ^d)\, \\| \\cdot \\|_{Q_s} )$\, showing that they are special cases of Kat
 snelson’s setting (only) for $s \\ge 0$.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tino Ullrich (Technische Universität Chemnitz)
DTSTART:20210325T144000Z
DTEND:20210325T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/24/">Consequences of the Kadison Singer solution and Weaver's conjectur
 e for the recovery of multivariate functions from a few random samples</a>
 \nby Tino Ullrich (Technische Universität Chemnitz) as part of Function s
 paces\n\n\nAbstract\nThe celebrated solution of the Kadison Singer problem
  by Markus\, Spielman and Srivastava in 2015 via Weaver’s conjecture is 
 the starting point for a new subsampling technique for finite frames in $C
 ^m$ by keeping the stability. We consider the special situation of a frame
  coming from a finite orthonormal system of $m$ functions evaluated at ran
 dom nodes (drawn from the orthogonality measure). It is well known that th
 is yields a good frame with high probability when we logarithmically overs
 ample\, i.e. take $n$ samples with $n = m log(m)$. By the mentioned subsam
 pling technique we may select a sub-frame of size $O(m)$. The consequence 
 is a new general upper bound for the minimal $L^2$-worst-case recovery err
 or in the framework of RKHS\, where only $n$ function samples are allowed.
  This quantity can be bounded in terms of the singular numbers of the comp
 act embedding into the space of square-integrable functions. It turns out 
 that in many relevant situations this quantity is asymptotically only wors
 e by square root of $log(n)$ compared to the singular numbers. The algorit
 hm which realizes this behavior is a weighted least squares algorithm base
 d on a specific set of sampling nodes which works for the whole class of f
 unctions simultaneously. These points are constructed out of a random draw
  with respect to distribution tailored to the spectral properties of the r
 eproducing kernel (importance sampling) in combination with a sub-sampling
  mentioned above. For the above multivariate setting\, it is still a funda
 mental open problem whether sampling algorithms are as powerful as algorit
 hms allowing general linear information like Fourier or wavelet coefficien
 ts. However\, the gap is now rather small.\n\nThis is joint work with N. N
 agel and M. Schaefer from TU Chemnitz.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Gibara (Université Laval\, Québec)
DTSTART:20210408T134000Z
DTEND:20210408T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/26/">The decreasing rearrangement and mean oscillation</a>\nby Ryan Gib
 ara (Université Laval\, Québec) as part of Function spaces\n\n\nAbstract
 \nIn joint work with Almut Burchard and Galia Dafni\, we study the bounded
 ness and continuity of the decreasing rearrangement on the space $\\operat
 orname{BMO}$ of functions of bounded mean oscillation in $\\mathbb{R}^n$. 
 Improvements on the operator bounds will be presented\, including recent p
 rogress bringing the $O(2^{n/2})$ bound to $O(\\sqrt{n})$. Then\, the fail
 ure of the continuity of decreasing rearrangement on $\\operatorname{BMO}$
  will be discussed\, along with some sufficient normalisation conditions t
 o guarantee continuity on the subspace $\\operatorname{VMO}$ of functions 
 of vanishing mean oscillation.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukáš Malý (Linköping University)
DTSTART:20210422T134000Z
DTEND:20210422T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/27/">Dirichlet problem for functions of least gradient in domains with 
 boundary of positive mean curvature in metric measure spaces</a>\nby Luká
 š Malý (Linköping University) as part of Function spaces\n\n\nAbstract\
 nSternberg\, Williams\, and Ziemer showed that the existence\, uniqueness\
 , and regularity of solutions to the Dirichlet problem for $1$-Laplacian o
 n domains in $R^n$ are closely related to the mean curvature of the domain
 's boundary. In my talk\, I will discuss the problem of minimization of th
 e corresponding energy functional\, which can be naturally formulated and 
 studied in the setting of $\\operatorname{BV}$ functions on metric measure
  spaces. Having generalized the notion of positive mean curvature of the b
 oundary\, one can prove the existence of solutions to the Dirichlet proble
 m. However\, solutions can fail to be continuous and/or unique even if the
  boundary and the boundary data are smooth\, which shall be demonstrated u
 sing fairly simple examples in weighted $R^2$.\n\nThe talk is based on joi
 nt work with Panu Lahti\, Nages Shanmugalingam\, and Gareth Speight\, with
  a contribution of Esti Durand-Cartagena and Marie Snipes.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Fernández Martínez (Universidad de Murcia)
DTSTART:20210401T134000Z
DTEND:20210401T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/28/">General Reiteration Theorems for $\\mathcal{R}$ and $\\mathcal{L}$
  spaces</a>\nby Pedro Fernández Martínez (Universidad de Murcia) as part
  of Function spaces\n\n\nAbstract\nThe results contained in this lecture a
 re part of an ongoing research project with T. Signes.  We will work with 
 the real interpolation method defined by means of slowly varying functions
  and rearrangement invariant (r.i.) spaces. More precisely\, for  $0 \\leq
  \\theta \\leq 1$\, $b$ a slowly varying function and $E$ an r.i. space we
  define the following interpolation space for the couple $\\overline{X} = 
 (X_{0}\, X_{1})$:\n$$\n    \\overline{X}_{\\theta\,\\operatorname{b}\,E}=\
 \Big\\{f\\in X_0+X_1\\\;\\colon\\\;\n    \\big \\| t^{-\\theta} {\\operato
 rname{b}}(t) K(t\,f) \\big \\|_{\\widetilde{E}} < \\infty\\Big\\}.\n$$\nTh
 is interpolation scale is stable under reiteration for $0 < \\theta <1$. I
 ndeed\, for\n$0 <\\theta < 1$ and $0<\\theta_0<\\theta_1<1$\,\n$$\n    \\b
 ig(  \\overline{X}_{\\theta_0\,\\operatorname{b}_0\,E_0}\, \\overline{X}_{
 \\theta_1\, \\operatorname{b}_{1}\, E_{1}} \\big)_{\\theta\, \\operatornam
 e{b}\, E}=\n    \\overline{X}_{\\tilde{\\theta}\,\\tilde{\\operatorname{b}
 }\,E}.\n$$\nHowever\, interpolation with parameter $\\theta=0$ or $\\theta
 =1$ gives rise to the $\\mathcal{L}$ and $\\mathcal{R}$ spaces:\n$$\n    \
 \Big(  \\overline{X}_{\\theta_0\,\\operatorname{b}_0\,E_0}\, \\overline{X}
 _{\\theta_1\,\\operatorname{b}_1\,E_1}  \\Big)_{0\,\\operatorname{b}\,E}=\
 n    \\overline{X}^{\\mathcal{L}}_{\\theta_0\,\\operatorname{b}\\circ\\rho
 \,E\,\\operatorname{b}_0\,E_0}\n$$\n$$\n    \\Big( \\overline{X}_{\\theta_
 0\,\\operatorname{b}_0\,E_0}\, \\overline{X}_{\\theta_1\,\\operatorname{b}
 _1\,E_1}\\Big)_{1\,\\operatorname{b}\,E}=\n    \\overline{X}^{\\mathcal{R}
 }_{\\theta_1\,\\operatorname{b}\\circ\\rho\,E\,\\operatorname{b}_1\,E_1}.\
 n$$\nHere\, we will present reiteration theorems that identify the spaces\
 n$$\n    \\Big(\\overline{X}^{\\mathcal R}_{\\theta_0\,\\operatorname{b}_0
 \,E_0\,a\,F}\, \\overline{X}_{\\theta_1\,\\operatorname{b}_1\,E_1}\\Big)_{
 \\theta\,\\operatorname{b}\,E}\n\\qquad\n    \\Big(\\overline{X}_{\\theta_
 0\,\\operatorname{b}_0\,E_0}\, \\overline{X}^{\\mathcal L}_{\\theta_1\, \\
 operatorname{b}_1\,E_1\,a\,F}\\Big)_{\\theta\,\\operatorname{b}\,E}\n$$\n$
 $\n    \\Big(\\overline{X}_{\\theta_0\,\\operatorname{b}_0\,E_0}\, \\overl
 ine{X}^{\\mathcal R}_{\\theta_1\, \\operatorname{b}_1\,E_1\,a\,F}\\Big)_{\
 \theta\,\\operatorname{b}\,E}\n\\qquad\n    \\Big(\\overline{X}^{\\mathcal
  L}_{\\theta_0\, \\operatorname{b}_0\,E_0\,a\,F}\, \\overline{X}_{\\theta_
 1\,\\operatorname{b}_1\,E_1}\\Big)_{\\theta\,\\operatorname{b}\,E}.\n$$\n\
 nWe illustrate the use of these results with applications to interpolation
  of\ngrand and small Lebesgue spaces\, Gamma spaces and $A$ and $B$-type s
 paces.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gael Diebou Yomgne (University of Bonn)
DTSTART:20210429T134000Z
DTEND:20210429T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/29/">Stationary Navier-Stokes flow with irregular Dirichlet data</a>\nb
 y Gael Diebou Yomgne (University of Bonn) as part of Function spaces\n\n\n
 Abstract\nIn this talk\, we discuss recent results on the well-posedness o
 f the\nforced Navier-Stokes equations in bounded/unbounded domain (in arbi
 trary\ndimension) subject to Dirichlet data assuming minimal smoothness\np
 roperties at the boundary. We will emphasize the construction of the\nsolu
 tion space which reflects the intrinsic features (scaling and\ntranslation
  invariance\, type of nonlinearity) of the equation. Our\nmachinery togeth
 er with some known facts in harmonic analysis and function\nspace theory p
 redicts a boundary class from a Triebel-Lizorkin scale. By\nprescribing sm
 all data\, existence\, uniqueness\, and regularity results are\nobtained u
 sing a non-variational approach. This solvability improves the\nprevious e
 xisting results which will be mentioned.\nIf time allows\, we will also di
 scuss the self-similarity properties of\nsolutions in a somewhat different
  setting.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nages Shanmugalingam (University of Cincinnati)
DTSTART:20210513T134000Z
DTEND:20210513T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/30/">Uniformization of weighted Gromov hyperbolic spaces and uniformly 
 locally bounded geometry</a>\nby Nages Shanmugalingam (University of Cinci
 nnati) as part of Function spaces\n\n\nAbstract\nThe seminal work of Bourd
 on and Pajot gave a way of constructing a Gromov hyperbolic space whose bo
 undary is a compact doubling metric space of interest. The work of Bonk\, 
 Heinonen\, and Koskela gave us a way of turning a Gromov hyperbolic space 
 into a uniform domain whose boundary is quasisymmetric to the original com
 pact doubling space. In this talk\, we will describe a way of uniformizing
  measures on a Gromov hyperbolic space that is uniformly locally doubling 
 and supports a uniformly local Poincare inequality to obtain a uniform spa
 ce that is equipped with a globally doubling measure supporting a global P
 oincare inequality. This is then used to compare Besov spaces on the origi
 nal compact doubling space with traces of Newton-Sobolev spaces on the uni
 form domain. This talk is based on joint work with Anders Bjorn and Jana B
 jorn.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktor Kolyada (Karlstad University)
DTSTART:20210520T134000Z
DTEND:20210520T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/31/">Estimates of Besov mixed-type norms for functions in Sobolev and H
 ardy-Sobolev spaces</a>\nby Viktor Kolyada (Karlstad University) as part o
 f Function spaces\n\n\nAbstract\nWe prove embeddings of Sobolev and Hardy-
 Sobolev spaces into Besov spaces built upon certain mixed norms. This give
 s an improvement of the known embeddings into usual Besov spaces. Applying
  these results\, we obtain Oberlin type estimates of Fourier transforms fo
 r functions in Sobolev spaces.\n\nPublished in: Ann. Mat. Pura Appl.\, 192
 \, no. 2 (2019)\, 615-637.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petru Mironescu (l’Institut Camille Jordan de l’Université Ly
 on 1)
DTSTART:20210603T134000Z
DTEND:20210603T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/32/">Sobolev maps to the circle</a>\nby Petru Mironescu (l’Institut C
 amille Jordan de l’Université Lyon 1) as part of Function spaces\n\n\nA
 bstract\nSobolev spaces $W^{s\, p}$ of maps with values into a compact man
 ifold naturally appear in geometry and material sciences. They exhibit qua
 litatively different properties from scalar Sobolev spaces: in general\, t
 here is no density of smooth maps\, and standard trace theory fails. We wi
 ll present some of their basic properties\, with a focus on the cases wher
 e $s<1$ or the target manifold is the circle\, in which harmonic analysis 
 tools combined with geometric considerations are quite effective. In parti
 cular\, we discuss the factorization of unimodular maps\, which can be see
 n as a geometric version of paraproducts.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Maria Martell (ICMAT\, Madrid)
DTSTART:20210527T134000Z
DTEND:20210527T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/33/">Distilling Rubio de Francia's extrapolation theorem</a>\nby Jose M
 aria Martell (ICMAT\, Madrid) as part of Function spaces\n\n\nAbstract\nRu
 bio de Francia's extrapolation theorem states that if a given operator is 
 bounded on $L^2(w)$ for all $w\\in A_2$\, then the same occurs on $L^p(w)$
  for all $w\\in A_p$ and for all $p\\in(1\,\\infty)$. Its proof only uses 
 the boundedness of the Hardy-Littlewood maximal function on weighted space
 s.  In this talk I will adopt a new viewpoint on which the desired estimat
 e follows from some "embedding" based on this basic ingredient. This allow
 s us to generalize extrapolation in the context of Banach function spaces 
 on which the some weighted estimates hold for the Hardy-Littlewood maximal
  function.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART:20210617T134000Z
DTEND:20210617T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/34/">Singular Brascamp-Lieb inequalities with cubical structure</a>\nby
  Polona Durcik (Chapman University) as part of Function spaces\n\n\nAbstra
 ct\nBrascamp-Lieb inequalities are Lp estimates for certain multilinear in
 tegral forms on functions on Euclidean spaces. They generalize several cla
 ssical inequalities\, such as Hoelder's inequality or Young's convolution 
 inequality. In this talk\, we focus on singular Brascamp-Lieb inequalities
 \, which arise when one of the functions in a Brascamp-Lieb integral is re
 placed by a singular integral kernel. Singular Brascamp-Lieb integrals are
  much less understood than their non-singular variants. We discuss some re
 sults and open problems in the area and focus on a special case which feat
 ures a particular cubical structure. Based on joint works with C. Thiele a
 nd work in progress with L. Slavíková and C. Thiele.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Van Schaftingen (Université catholique de Louvain)
DTSTART:20210701T134000Z
DTEND:20210701T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/35/">Estimates for the Hopf invariant in critical fractional Sobolev sp
 aces</a>\nby Jean Van Schaftingen (Université catholique de Louvain) as p
 art of Function spaces\n\n\nAbstract\nThe Brouwer degree classifies the ho
 motopy classes of mappings from a sphere into itself. Bourgain\, Brezis an
 d Mironescu have obtained some linear estimates of the degree of a mapping
  by any critical first-order or fractional Sobolev energy. Similarly\, map
 s from the three-dimensional sphere to the two-dimensional spheres are cla
 ssified by their Hopf invariant. Thanks to the Whitehead formula\, Riviere
  has proved a sharp nonlinear control of the Hopf invariant by the first-o
 rder critical Sobolev energy. I will explain how a general compactness arg
 ument implies that sets that have bounded critical fractional Sobolev ener
 gy have bounded Hopf invariant and how we are obtaining in collaboration w
 ith Armin Schikorra sharp nonlinear estimates in critical fractional Sobol
 ev spaces with order is close to 1.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ritva Hurri-Syrjänen (University of Helsinki)
DTSTART:20210624T134000Z
DTEND:20210624T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/36/">On the John-Nirenberg space</a>\nby Ritva Hurri-Syrjänen (Univers
 ity of Helsinki) as part of Function spaces\n\n\nAbstract\nFritz John and 
 Louis Nirenberg gave a summation condition for cubes\nwhich gives rise to 
 a function space. This $\\operatorname{JN}_p$ space has been less well\nkn
 own than the $\\operatorname{BMO}$ space. The talk will address questions 
 related\nto functions belonging to the $\\operatorname{JN}_p$ space when t
 he functions are defined\non certain domains in $R^n$.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Santeri Miihkinen (Karlstad University)
DTSTART:20210506T134000Z
DTEND:20210506T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/37/">The infinite Hilbert matrix on spaces of analytic functions</a>\nb
 y Santeri Miihkinen (Karlstad University) as part of Function spaces\n\n\n
 Abstract\nThe (finite) Hilbert matrix is arguably one of the single most w
 ell-known matrices in mathematics. The infinite Hilbert matrix $\\mathcal 
 H$ was introduced by David Hilbert around 120 years ago in connection to h
 is double series theorem. It can be interpreted as a linear operator on sp
 aces of analytic functions by its action on their Taylor coefficients. The
  boundedness of $\\mathcal H$ on the Hardy spaces $H^p$ for $1 < p < \\inf
 ty$ and Bergman spaces $A^p$ for $2 < p < \\infty$ was established by Diam
 antopoulos and Siskakis. The exact value of the operator norm of $\\mathca
 l H$ acting on the Bergman spaces $A^p$ for $4 \\le p < \\infty$ was shown
  to be $\\frac{\\pi}{\\sin(2\\pi/p)}$ by Dostanic\, Jevtic and Vukotic in 
 2008. The case $2 < p < 4$ was an open problem until in 2018 it was shown 
 by Bozin and Karapetrovic that the norm has the same value also on the sca
 le $2 < p < 4$. In this talk\, we review some of the old results and consi
 der the still partly open problem regarding the value of the norm on weigh
 ted Bergman spaces. The talk is partly based on joint work with Mikael Lin
 dström and Niklas Wikman (Åbo Akademi).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianluigi Manzo (University of Naples)
DTSTART:20210610T134000Z
DTEND:20210610T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/38/">The spaces $BMO_{(s)}$ and o-O structures</a>\nby Gianluigi Manzo 
 (University of Naples) as part of Function spaces\n\n\nAbstract\nIn 2015 a
  new Banach space $B$ was introduced by Bourgain\, Brezis and Mironescu\, 
 equipped with a norm defined as a supremum of oscillations. This space has
  a subspace $B_0$ which has a vanishing condition the oscillations and who
 se bidual is exactly $B$. This situation is similar to what happens with t
 he $(VMO\,BMO)$: in fact\, there are many Banach spaces $E$\, defined by a
  supremum ("big o") condition that are biduals of a subspace $E_0$ defined
  by a vanishing ("little o") condition. The space $B$ sparked the interest
  in these spaces\, with the help of a construction due to K. M. Perfekt. T
 his talk aims to give a brief overview on some results on these o-O pairs\
 , with a focus on the family of spaces $BMO_{(s)}$ recently introduced by 
 C. Sweezy.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loukas Grafakos (University of Missouri\, Columbia)
DTSTART:20220203T144000Z
DTEND:20220203T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/39/">From Fourier series to multilinear analysis</a>\nby Loukas Grafako
 s (University of Missouri\, Columbia) as part of Function spaces\n\n\nAbst
 ract\nWe present a survey of classical results related to summability of F
 ourier series. We indicate how the question of summability of products of 
 Fourier series motivates the study of multilinear analysis\, in particular
  the study of multilinear multiplier problems. We discuss some new results
  in this area and outline our methodology.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergi Baena Miret (University of Barcelona\, Spain)
DTSTART:20220210T144000Z
DTEND:20220210T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/40/">Decreasing rearrangements on average operators</a>\nby Sergi Baena
  Miret (University of Barcelona\, Spain) as part of Function spaces\n\n\nA
 bstract\nLet $\\{T_\\theta\\}_\\theta$ be a family of operators indexed in
  a probability measure space $(\\Omega\, \\mathcal A\, P)$ such that the b
 oundedness $$T_\\theta:L^1(u) \\longrightarrow  L^{1\, \\infty}(u)\, \\qqu
 ad \\forall u \\in A_1\,\n$$ holds with constant less than or equal to $\\
 varphi(\\lVert u \\rVert_{A_1})$\, with $\\varphi$ being a nondecreasing f
 unction on $(0\,\\infty)$ and where $A_1$ is the class of Muckenhoupt weig
 hts. The aim of this talk is to address the following two questions: what 
 can we say about the  decreasing rearrangement of the average operator\n$$
 T_A f(x)= \\int_{\\Omega} T_\\theta f(x) dP(\\theta)\, \\qquad x \\in \\ma
 thbb R^n\,$$ whenever is well defined and what can we say about its bounde
 dness over r.i. spaces as\, for instance\, the classical Lorentz spaces?\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Spector (National Taiwan Normal University)
DTSTART:20220217T144000Z
DTEND:20220217T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/41/">An Atomic Decomposition for Divergence Free Measures</a>\nby Danie
 l Spector (National Taiwan Normal University) as part of Function spaces\n
 \n\nAbstract\nIn this talk\, we describe a recent result obtained in colla
 boration with Felipe Hernandez where we give an atomic decomposition for t
 he space of divergence-free measures. The atoms in this setting are piecew
 ise $C^1$ closed curves which satisfy a ball growth condition\, while our 
 result can be used to deduce certain "forbidden" Sobolev inequalities whic
 h arise in the study of electricity and magnetism.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Rosario Mingione (Universita di Parma\, Italy)
DTSTART:20220224T144000Z
DTEND:20220224T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/42/">Perturbations beyond Schauder</a>\nby Giuseppe Rosario Mingione (U
 niversita di Parma\, Italy) as part of Function spaces\n\n\nAbstract\nSo-c
 alled Schauder estimates are a standard tool in the analysis of linear ell
 iptic and parabolic PDEs. They had been originally proved by Hopf (1929\, 
 interior case)\, and by Schauder and Caccioppoli (1934\, global estimates)
 . Since then\, several proofs were given (Campanato\, Trudinger\, Simon). 
 The nonlinear case is a more recent achievement from the 80s (Giaquinta & 
 Giusti\, Ivert\, J. Manfredi\, Lieberman). All these classical results tak
 e place in the uniformly elliptic case. I will discuss progress in the non
 uniformly elliptic one. From joint work with Cristiana De Filippis.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Kh. Balci (Universität Bielefeld\, Germany)
DTSTART:20220324T144000Z
DTEND:20220324T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/43/">(Generalized) Sobolev-Orlicz Spaces of differential forms</a>\nby 
 Anna Kh. Balci (Universität Bielefeld\, Germany) as part of Function spac
 es\n\n\nAbstract\nWe  study  generalised Sobolev-Orlicz spaces of differen
 tial forms. In particular we provide results on density of smooth function
 s and design examples on Lavrentiev gap for partial spaces of differential
  forms such as variable exponent\, double phase and weighted energy.  As a
 n application we consider Lavrentiev gap for so-called borderline case of 
 double phase potential model.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Karlovich (NOVA University Lisbon\, Portugal)
DTSTART:20211104T144000Z
DTEND:20211104T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/44/">On the interpolation constants for variable Lebesgue spaces</a>\nb
 y Alexei Karlovich (NOVA University Lisbon\, Portugal) as part of Function
  spaces\n\n\nAbstract\nFor $\\theta\\in(0\,1)$ and variable exponents $p_0
 (\\cdot)\,q_0(\\cdot)$ and\n$p_1(\\cdot)\,q_1(\\cdot)$ with values in $[1\
 ,\\infty]$\, let the variable exponents\n$p_\\theta(\\cdot)\,q_\\theta(\\c
 dot)$ be defined by\n\\[\n1/p_\\theta(\\cdot):=(1-\\theta)/p_0(\\cdot)+\\t
 heta/p_1(\\cdot)\,\n\\quad\n1/q_\\theta(\\cdot):=(1-\\theta)/q_0(\\cdot)+\
 \theta/q_1(\\cdot).\n\\]\nThe Riesz-Thorin type interpolation theorem for 
 variable Lebesgue spaces says\nthat if a linear operator $T$ acts boundedl
 y from the variable Lebesgue space\n$L^{p_j(\\cdot)}$ to the variable Lebe
 sgue space $L^{q_j(\\cdot)}$ for $j=0\,1$\,\nthen\n\\[\n\\|T\\|_{L^{p_\\th
 eta(\\cdot)}\\to L^{q_\\theta(\\cdot)}}\n\\le\nC\n\\|T\\|_{L^{p_0(\\cdot)}
 \\to L^{q_0(\\cdot)}}^{1-\\theta}\n\\|T\\|_{L^{p_1(\\cdot)}\\to L^{q_1(\\c
 dot)}}^{\\theta}\,\n\\]\nwhere $C$ is an interpolation constant independen
 t of $T$. We consider two\ndifferent modulars $\\varrho^{\\max}(\\cdot)$ a
 nd $\\varrho^{\\rm sum}(\\cdot)$\ngenerating variable Lebesgue spaces and 
 give upper estimates for the\ncorresponding interpolation constants $C_{\\
 rm max}$ and $C_{\\rm sum}$\,\nwhich imply that $C_{\\rm max}\\le 2$ and $
 C_{\\rm sum}\\le 4$\, as well as\, lead\nto sufficient conditions for $C_{
 \\rm max}=1$ and $C_{\\rm sum}=1$. We also\nconstruct an example showing t
 hat\, in many cases\, our upper estimates are\nsharp and the interpolation
  constant is greater than one\, even if one requires\nthat $p_j(\\cdot)=q_
 j(\\cdot)$\, $j=0\,1$ are Lipschitz continuous and bounded\naway from one 
 and infinity (in this case\n$\\varrho^{\\rm max}(\\cdot)=\\varrho^{\\rm su
 m}(\\cdot)$).\nThis is a joint work with Eugene Shargorodsky (King's Colle
 ge London\, UK).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joao Pedro G. Ramos (ETH Zürich\, Switzerland)
DTSTART:20211111T144000Z
DTEND:20211111T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/45/">Stability for geometric and functional inequalities</a>\nby Joao P
 edro G. Ramos (ETH Zürich\, Switzerland) as part of Function spaces\n\n\n
 Abstract\nThe celebrated isoperimetric inequality states that\, for a meas
 urable set $S \\subset \\R^n\,$ the inequality\n\\[\n\\text{per}(S) \\ge n
  \\text{vol}(S)^{\\frac{n-1}{n}} \\text{vol}(B_1)^{\\frac{1}{n}}\n\\]\nhol
 ds\, where $\\text{per}(S)$ denotes the perimeter (or surface area) of $S\
 ,$ and equality holds if and only if $S$ is an euclidean ball. This result
  has many applications throughout analysis\, but an interesting feature is
  that it can be obtained as a corollary of a more general inequality\, the
  Brunn--Minkowski theorem: if $A\,B \\subset \\R^n\,$ define $A+B = \\{ a+
 b\, a \\in A\, b\\in B\\}.$ Then\n\\[\n|A+B|^{1/n} \\ge |A|^{1/n} + |B|^{1
 /n}.\n\\]\nHere\, equality holds if and only if $A$ and $B$ are homothetic
  and convex. A question pertaining to both these results\, that aims to ex
 ploit deeper features of the geometry behind them\, is that of stability: 
 if $S$ is close to being optimal for the isoperimetric inequality\, can we
  say that $A$ is close to being a ball? Analogously\, if $A\,B$ are close 
 to being optimal for Brunn--Minkowski\, can we say they are close to being
  compact and convex?\n\nThese questions\, as stand\, have been answered on
 ly in very recent efforts by several mathematicians. In this talk\, we sha
 ll outline these results\, with focus on the following new result\, obtain
 ed jointly with A. Figalli and K. B\\"or\\"oczky. If $f\,g$ are two non-ne
 gative measurable functions on $\\R^n\,$ and $h:\\R^n \\to \\R_{\\ge 0}$ i
 s measurable such that\n\\[\nh(x+y) \\ge f(2x)^{1/2} g(2y)^{1/2}\, \\\, \\
 forall x\,y \\in \\R^n\,\n\\]\nthen the Prekopa--Leindler inequality asser
 ts that\n\\[\n\\int h \\ge \\left(\\int f\\right)^{1/2} \\left( \\int g\\r
 ight)^{1/2}\,\n\\]\nwhere equality holds if and only if $h$ is log-concave
 \, and $f\,g$ are `homothetic' to $h$\, in a suitable sense. We prove that
 \, if $\\int h \\le (1+\\varepsilon) \\left(\\int f\\right)^{1/2} \\left( 
 \\int g\\right)^{1/2}\,$ then $f\,g\,h$ are $\\varepsilon^{\\gamma_n}-$ $L
 ^1-$close to being optimal. We will discuss the general idea for the proof
  and\, time-allowing\, discuss on a conjectured sharper version.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iwona Chlebicka (Institute of Applied Mathematics and Mechanics\, 
 University of Warsaw\, Poland)
DTSTART:20211118T144000Z
DTEND:20211118T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/46/">Approximation properties of Musielak-Orlicz-Sobolev spaces and its
  role in well-posedness of nonstandard growth PDE</a>\nby Iwona Chlebicka 
 (Institute of Applied Mathematics and Mechanics\, University of Warsaw\, P
 oland) as part of Function spaces\n\n\nAbstract\nMusielak-Orlicz-Sobolev s
 paces describe in one framework Sobolev spaces with variable exponent\, wi
 th double phase\, as well as isotropic and anisotropic Orlicz spaces. Ther
 e is significant interest in PDEs and calculus of variations fitting in su
 ch a framework. These spaces share an essential difficulty - smooth functi
 ons are not dense in Musielak-Orlicz-Sobolev spaces unless the function ge
 nerating them is regular enough. It is closely related to the so-called La
 vrentiev's phenomenon describing the situation when infima of a variationa
 l functional over regular functions and over all functions in the energy s
 pace are different. Throughout the talk I will be explaining in detail why
  for PDEs it is so critical to have density especially in non-reflexive sp
 aces.\n\nThe typical examples of sufficient conditions for the density is 
 log-H\\"older continuity of the variable exponent or the closeness conditi
 on for powers in the double phase spaces. Some sufficient conditions were 
 known in the anisotropic cases\, but they were not truly capturing full an
 isotropy. I will present new sufficient conditions obtained in collaborati
 on with Michał Borowski (student at University of Warsaw). They improve p
 revious conditions covering all known optimal conditions and being essenti
 ally better than any non-doubling or anisotropic condition before.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fraccaroli (University of Bonn\, Germany)
DTSTART:20211209T144000Z
DTEND:20211209T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/47/">Outer $L^p$ spaces: Köthe duality\, Minkowski inequality and more
 </a>\nby Marco Fraccaroli (University of Bonn\, Germany) as part of Functi
 on spaces\n\n\nAbstract\nThe theory of $L^p$ spaces for outer measures\, o
 r outer $L^p$ spaces\, was\ndeveloped by Do and Thiele to encode the proof
  of boundedness of certain\nmultilinear operators in a streamlined argumen
 t. Accordingly to this\npurpose\, the theory was developed in the directio
 n of the real\ninterpolation features of these spaces\, such as versions o
 f H\\"{o}lder's\ninequality and Marcinkiewicz interpolation\, while other 
 questions remained\nuntouched.\n\nFor example\, the outer $L^p$ spaces are
  defined by quasi-norms\ngeneralizing the classical mixed $L^p$ norms on s
 ets with a Cartesian\nproduct structure\; it is then natural to ask whethe
 r in arbitrary settings\nthe outer $L^p$ quasi-norms are equivalent to nor
 ms and what other\nreasonable properties they satisfy\, e.g. K\\"{o}the du
 ality and Minkowski\ninequality. In this talk\, we will answer these quest
 ions\, with a\nparticular focus on two specific settings on the collection
  of dyadic\nintervals in $\\mathbb{R}$ and the collection of dyadic Heisen
 berg boxes in\n$\\mathbb{R}^2$. This will allow us to clarify the relation
  between outer\n$L^p$ spaces and tent spaces\, and get a glimpse at the us
 e of this\nlanguage in the proof of boundedness of prototypical multilinea
 r operators\nwith invariances.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Cameron Campbell (University of Hradec Králové)
DTSTART:20211216T144000Z
DTEND:20211216T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/48/">Closures of planar BV homeomorphisms and the relaxation of functio
 nals with linear growth</a>\nby Daniel Cameron Campbell (University of Hra
 dec Králové) as part of Function spaces\n\n\nAbstract\nMotivated by rela
 xation results of Kristensen and Rindler\, and of Benešová\, Krömer and
  Kružík for BV maps\, we study the class of strict limits of BV planar h
 omeomorphisms. We show that\, although such maps need not be injective and
  are not necessarily continuous on almost every line\, the class has a rea
 sonable behavior expected for limit of elastic deformations. By a characte
 rization of the classes of strict and area-strict limits of BV homeomorphi
 sms we show that these classes coincide.\n\nThis is based on joint works w
 ith S. Hencl\, A. Kauranen and E. Radici.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franz Gmeineder (University of Konstanz\, Germany)
DTSTART:20220106T144000Z
DTEND:20220106T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/49/">A-quasiconvexity\, function spaces and regularity</a>\nby Franz Gm
 eineder (University of Konstanz\, Germany) as part of Function spaces\n\n\
 nAbstract\nBy Morrey's foundational work\, quasiconvexity displays a key\n
 notion in the vectorial Calculus of Variations. A suitable generalisation\
 nthat keeps track of more elaborate differential conditions is given by\nF
 onseca \\& Müller's $\\mathcal{A}$-quasiconvexity. With the topic having\
 nfaced numerous contributions as to lower semicontinuity\, in this talk I\
 ngive an overview of recent results for such problems with focus on the\nu
 nderlying function spaces and the (partial) regularity of minima.\n\nThe t
 alk is partially based on joint work with Sergio Conti (Bonn)\,\nLars Dien
 ing (Bielefeld)\, Bogdan Raita (Pisa) and Jean Van Schaftingen\n(Louvain).
 \n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Baroni (University of Parma\, Italy)
DTSTART:20220113T144000Z
DTEND:20220113T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/50/">New results for non-autonomous functionals with mild phase transit
 ion</a>\nby Paolo Baroni (University of Parma\, Italy) as part of Function
  spaces\n\n\nAbstract\nWe describe how different regularity assumptions on
  the x-dependence of the energy impact the regularity of minimizers of som
 e non-autonomous functionals having nonuniform ellipticity of moderate siz
 e. We put particular emphasis on double phase functionals with logarithmic
  phase transition\, including some new results.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Pawlewicz (University of Warsaw\, Poland)
DTSTART:20220120T144000Z
DTEND:20220120T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/51/">On the Embedding of BV Space into Besov-Orlicz Space</a>\nby Aleks
 ander Pawlewicz (University of Warsaw\, Poland) as part of Function spaces
 \n\n\nAbstract\nDuring the presentation I will give a sufficient (and\, in
  the case of a compact domain\, necessary) condition for the boundedness o
 f the embedding operator from $BV(\\Omega)$ space (the space of integrable
  functions for which a weak gradient exists and is a Radon measure) into B
 esov-Orlicz space $B_{\\varphi\,1}^\\psi(\\Omega)$\, where $\\Omega\\subse
 teq\\mathbb{R}^d$. The condition has a form of an integral inequality invo
 lving a Young function $\\varphi$ and a weight function $\\psi$ and can be
  written as follows \n\\[\n\\frac{s^{d-1}}{\\varphi^{-1}(s^d)}\\int_0^s\\f
 rac{\\psi(1/t)}{t}dt + \\int_s^\\infty\\frac{\\psi(1/t)s^{d-1}}{\\varphi^{
 -1}(ts^{d-1})t} dt < D\,\n\\]\nfor some constant $D>0$ and every $s>0$. Th
 e main tool of the proof will be the molecular decomposition of functions 
 from $BV$ space.\n\nThe talk will be based on a joint work with Michał Wo
 jciechowski. Our paper "On the Embedding of BV Spaces into Besov-Orlicz Sp
 ace" is already available on arXiv.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Ferone (University of Naples Federico II\, Italy)
DTSTART:20220127T144000Z
DTEND:20220127T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/52/">Symmetrization for fractional elliptic problems: a direct approach
 </a>\nby Vincenzo Ferone (University of Naples Federico II\, Italy) as par
 t of Function spaces\n\n\nAbstract\nWe provide new direct methods to estab
 lish symmetrization results in the form of mass concentration (\\emph{i.e.
 } integral) comparison for fractional elliptic equations of the type $(-\\
 Delta)^{s}u=f$ $(0 < s< 1 )$ in a bounded domain $\\Omega$\, equipped with
  homogeneous {Dirichlet }boundary conditions. The classical pointwise Tale
 nti rearrangement inequality is recovered in the limit $s\\rightarrow1$. F
 inally\, explicit counterexamples constructed for all $s\\in(0\,1)$ highli
 ght that the same pointwise estimate cannot hold in a nonlocal setting\, t
 hus showing the optimality of our results. This is a joint work with Bruno
  Volzone.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Hytönen (University of Helsinki)
DTSTART:20220310T144000Z
DTEND:20220310T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/53/">One-sided sparse domination</a>\nby Tuomas Hytönen (University of
  Helsinki) as part of Function spaces\n\n\nAbstract\nOver the past ten yea
 rs\, sparse domination has proven to be an efficient way to capture many k
 ey features of singular operators. Much of current research is about exten
 ding the method to ever more general classes of operators. The objects of 
 this talk are somewhat against this trend: to dominate more specific opera
 tors\, but then to have these special features reflected in the estimates.
  More concretely\, we deal with ``one-sided" (or ``causal") operators such
  that $Tf(x)$ only depends on the function $f$ on one side of the point $x
 $. Is it then possible to obtain a sparse bound with the same kind of caus
 ality? The dream theorem that one could hope for remains open\, but we are
  able to get a certain weaker version. This version is still good enough t
 o obtain the boundedness of one-sided operators in some function spaces\, 
 relevant for partial differential equations\, where usual "two-sided" oper
 ators are not bounded in general.\n\nThe talk is based on joint work with 
 Andreas Rosén (https://arxiv.org/abs/2108.10597).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Raita (Scuola Normale Superiore\, Pisa\, Italy)
DTSTART:20220317T144000Z
DTEND:20220317T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/54/">Nonlinear spaces of functions and compensated compactness for conc
 entrations</a>\nby Bogdan Raita (Scuola Normale Superiore\, Pisa\, Italy) 
 as part of Function spaces\n\n\nAbstract\nWe study compensation phenomena 
 for fields satisfying both a pointwise\nand a linear differential constrai
 nt. The compensation effect takes the form of nonlinear\nelliptic estimate
 s\, where constraining the values of the field to lie in a cone compensate
 s\nfor the lack of ellipticity of the differential operator. We give a ser
 ies of new examples of\nthis phenomenon\, focusing on the case where the c
 one is a subset of the space of symmetric matrices and the differential op
 erator is the divergence or the curl. One of our main\nfindings is that th
 e maximal gain of integrability is tied to both the differential operator\
 nand the cone\, contradicting in particular a recent conjecture from <a hr
 ef='https://arxiv.org/abs/2106.03077'>arXiv:2106.03077</a>.\nThis appends 
 the classical compensated compactness framework for oscillations with a\nv
 ariant designed for concentrations\, and also extends the recent theory of
  compensated\nintegrability due to D. Serre. In particular\, we find a new
  family of integrands that are\nDiv-quasiconcave under convex constraints\
 n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Koch (Max Planck Institute Mathematics in the Sciences\, Lei
 pzig)
DTSTART:20220303T144000Z
DTEND:20220303T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/55/">Functionals with nonstandard growth and convex duality</a>\nby Luk
 as Koch (Max Planck Institute Mathematics in the Sciences\, Leipzig) as pa
 rt of Function spaces\n\n\nAbstract\nI will present recent results obtaine
 d in collaboration with Jan Kristensen\n(Oxford) and Cristiana de Filippis
  (Parma) concerning functionals of the\nform\n\\[\n\\min_{u\\in g+W^{1\,p}
 _0 (\\Omega\,\\mathbb R^n)} \\int_{\\Omega}F(Du)\\\,dx\,\n\\]\nwhere $F(z)
 $ satisfies $(p\,q)$-growth conditions. In particular\, I will highlight h
 ow ideas from convex duality theory can be used in order to show\n$L^1$-re
 gularity of the stress $\\partial_z F(Du)$ and the validity of the Euler--
 Lagrange\nequation without an upper growth bound on $F(x\,\\cdot)$ as soon
  as $F(z)$ is convex\, proper\, essentially smooth and superlinear in $z$.
  Further\, I will give a\nexample of how to use similar ideas to obtain $W
 ^{1\,q}$-regularity of minimisers\nunder controlled duality $(p\, q)$-grow
 th with $2 \\le p \\le q \\le \\frac{np}{n-2}$.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Schwarzacher (University of Uppsala\, Sweden)
DTSTART:20220331T134000Z
DTEND:20220331T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/56/">Construction of a right inverse for the divergence in non-cylindri
 cal time dependent domains</a>\nby Sebastian Schwarzacher (University of U
 ppsala\, Sweden) as part of Function spaces\n\n\nAbstract\nWe discuss the 
 construction of a stable right inverse for the divergence operator in non-
 cylindrical domains in space-time. The domains are assumed to be Hölder r
 egular in space and evolve continuously in time. The inverse operator is o
 f Bogovskij type\, meaning that it attains zero boundary values. We provid
 e estimates in Sobolev spaces of positive and negative order with respect 
 to both time and space variables. The regularity estimates on the operator
  depend on the assumed Hölder regularity of the domain. The results can n
 aturally be connected to the known theory for Lipschitz domains. As an app
 lication\, we prove refined pressure estimates for weak and very weak solu
 tions to Navier-Stokes equations in time-dependent domains. This is a join
 t work with Olli Saari.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Hastö (University of Turku)
DTSTART:20220414T134000Z
DTEND:20220414T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/57/">Anisotropic generalized Orlicz spaces and PDE</a>\nby Peter Hastö
  (University of Turku) as part of Function spaces\n\n\nAbstract\nVector-va
 lued generalized Orlicz spaces can be divided into anisotropic\, quasi-iso
 tropic and isotropic. In isotropic spaces\, the Young function depends onl
 y on\nthe length of the vector\, i.e. $\\Phi(v)=\\phi(|v|)$. In the quasi-
 isotropic case $\\Phi(v)\\approx \\phi(v|)$ so the dependence is via the l
 ength of the vector up to a constant. In the anisotropic case\, there is n
 o such restriction\, and the Young function depends directly on the vector
 .\n\nBasic assumptions in anisotropic generalized Orlicz spaces are not as
  well understood as in the isotropic case. In this talk I explain the assu
 mptions and prove the equivalence of two widely used conditions in the the
 ory of generalized Orlicz spaces\, usually called (A1) and (M). This provi
 des a more natural and easily verifiable condition for use in the theory o
 f anisotropic generalized Orlicz spaces for results such as Jensen's inequ
 ality.\n\nIn collaboration with Jihoon Ok\, we obtained maximal local regu
 larity results of weak solutions or minimizers of\n\\[\n\\operatorname{div
 } A(x\, Du)=0\n\\quad\\text{and}\\quad\n\\min_u \\int_\\Omega F(x\,Du)\\\,
 dx\,\n\\]\nwhen $A$ or $F$ are general quasi-isotropic Young functions. In
  other words\, we studied the problem without recourse to special function
  structure and without\nassuming Uhlenbeck structure. We established local
  $C^{1\,\\alpha}$-regularity for some $\\alpha\\in(0\,1)$ and $C^{\\alpha}
 $-regularity for any $\\alpha\\in(0\,1)$ of weak solutions and local minim
 izers. Previously known\, essentially optimal\, regularity results are inc
 luded as special cases.\n\nPreprints are available at https://www.problems
 olving.fi/pp/.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton University)
DTSTART:20220505T134000Z
DTEND:20220505T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/58/">Nikodym-type spherical maximal functions</a>\nby Alan Chang (Princ
 eton University) as part of Function spaces\n\n\nAbstract\nWe study $L^p$ 
 bounds on Nikodym maximal functions associated to spheres. In contrast to 
 the spherical maximal functions studied by Stein and Bourgain\, our maxima
 l functions are uncentered: for each point in $\\mathbb R^n$\, we take the
  supremum over a family of spheres containing that point.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ruzhansky (Ghent University\, Belgium)
DTSTART:20220421T134000Z
DTEND:20220421T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/60/">Subelliptic pseudo-differential calculus on compact Lie groups</a>
 \nby Michael Ruzhansky (Ghent University\, Belgium) as part of Function sp
 aces\n\n\nAbstract\nIn this talk we will give an overview of several relat
 ed pseudo-differential theories and give a comparison for them in terms of
  regularity estimates\, on compact and nilpotent groups\, also contrasting
  the cases of elliptic and sub elliptic classes in the compact case.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank (California Institute of Technology)
DTSTART:20220407T134000Z
DTEND:20220407T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/61/">Sobolev spaces and spectral asymptotics for commutators</a>\nby Ru
 pert Frank (California Institute of Technology) as part of Function spaces
 \n\n\nAbstract\nWe discuss two different\, but related topics. The first c
 oncerns a new\, derivative-free characterization of homogeneous\, first-or
 der Sobolev spaces\, the second concerns spectral properties of so-called 
 quantum derivatives\, which are commutators with a certain singular integr
 al operator. At the endpoint\, these two topics come together and we try t
 o explain the analogy between the results and the proofs\, as well as an o
 pen conjecture.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Óscar Domínguez (Université Claude Bernard Lyon 1)
DTSTART:20220428T134000Z
DTEND:20220428T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/62/">New estimates for the maximal functions and applications</a>\nby 
 Óscar Domínguez (Université Claude Bernard Lyon 1) as part of Function 
 spaces\n\n\nAbstract\nWe discuss sharp pointwise inequalities for maximal 
 operators\, in\nparticular\, an extension of DeVore’s inequality for the
  moduli of\nsmoothness and a logarithmic variant of Bennett–DeVore–Sha
 rpley’s\ninequality for rearrangements.\nThis is joint work with Sergey 
 Tikhonov.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Glenn Byrenheid (Friedrich-Schiller University\, Jena (Germany))
DTSTART:20220519T134000Z
DTEND:20220519T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/63/">Sparse approximation for break of scale embeddings</a>\nby Glenn B
 yrenheid (Friedrich-Schiller University\, Jena (Germany)) as part of Funct
 ion spaces\n\n\nAbstract\nWe study sparse approximation of Sobolev type fu
 nctions having dominating mixed smoothness regularity borrowed for instanc
 e from the theory of solutions for the electronic Schrödinger equation. O
 ur focus is on measuring approximation errors in the practically relevant 
 energy norm. We compare the power of approximation for linear and non-line
 ar methods working on a dictionary of Daubechies wavelet functions. Explic
 it (non-)adaptive algorithms are derived that generate n-term approximants
  having dimension-independent rates of convergence.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angkana Rüland (Heidelberg University)
DTSTART:20220512T134000Z
DTEND:20220512T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/64/">On Rigidity\, Flexibility and Scaling Laws: The Tartar Square</a>\
 nby Angkana Rüland (Heidelberg University) as part of Function spaces\n\n
 \nAbstract\nIn this talk I will discuss a dichotomy between rigidity and f
 lexibility for certain differential inclusions from materials science and 
 the role of function spaces in this dichotomy: While solutions in sufficie
 ntly regular function spaces are ``rigid'' and are determined by the ``cha
 racteristics'' of the underlying equations\, at low regularity this is los
 t and a plethora of ``wild'' irregular solutions exist. I will show that t
 he scaling of certain energies could serve as a mechanism distinguishing t
 hese two regimes and may yield function spaces that separate these regimes
 . By discussing the Tartar square\, I will present an example of a situati
 on with a dichotomy between rigidity and flexibility where such scaling re
 sults can be proved.\n\nThis is based on joint work with Jamie Taylor\, An
 tonio Tribuzio\, Christian Zillinger and Barbara Zwicknagl.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wentao Teng (Kwansei Gakuin University)
DTSTART:20220526T134000Z
DTEND:20220526T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/65/">Dunkl translations\, Dunkl--type $BMO$ space and Riesz transforms 
 for Dunkl transform on $L^\\infty$</a>\nby Wentao Teng (Kwansei Gakuin Uni
 versity) as part of Function spaces\n\n\nAbstract\nWe study some results o
 n the support of Dunkl translations on compactly supported functions. Then
  we will define Dunkl--type $BMO$ space and Riesz transforms for Dunkl tra
 nsform on $L^\\infty$\, and prove the boundedness of Riesz transforms from
  $L^\\infty$ to Dunkl--type $BMO$ space under the uniform boundedness assu
 mption of Dunkl translations. The proof and the definition in Dunkl settin
 g will be harder than in the classical case for the lack of some similar p
 roperties of Dunkl translations to that of classical translations. We will
  also extend the preciseness of the description of support of Dunkl transl
 ations on characteristic functions by Gallardo and Rejeb to that on all no
 nnegative radial functions in $L^2(m_k)$.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olli Tapiola (Universitat Autònoma de Barcelona)
DTSTART:20221013T134000Z
DTEND:20221013T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/66/">John conditions\, Harnack chains and boundary Poincaré inequaliti
 es</a>\nby Olli Tapiola (Universitat Autònoma de Barcelona) as part of Fu
 nction spaces\n\n\nAbstract\nWe consider connections between the local Joh
 n condition\, the Harnack chain condition and weak boundary Poincaré ineq
 ualities in an open set $\\Omega \\subset \\mathbb{R}^{n+1}$ with $n$-dime
 nsional Ahlfors--David regular boundary. First\, we show that if $\\Omega$
  satisfies both the local John condition and the exterior corkscrew condit
 ion\, then $\\Omega$ also satisfies the Harnack chain condition (and hence
 \, is a chord-arc domain). Second\, we show that if $\\Omega$ is a 2-sided
  chord-arc domain\, then the boundary $\\partial \\Omega$ supports a Heino
 nen--Koskela-type weak $p$-Poincaré inequality for any $1 \\le p < \\inft
 y$. We also discuss the optimality of our assumptions and some follow-up q
 uestions. This is a joint work with Xavier Tolsa.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Weidner (Universitat de Barcelona)
DTSTART:20221027T134000Z
DTEND:20221027T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/67/">Regularity for nonlocal problems with non-standard growth</a>\nby 
 Marvin Weidner (Universitat de Barcelona) as part of Function spaces\n\n\n
 Abstract\nIn this talk\, we study robust regularity estimates for local mi
 nimizers of nonlocal functionals with non-standard growth of (p\,q)-type. 
 Our main focus is on Hölder regularity estimates and full Harnack inequal
 ities. Moreover\, our results apply to weak solutions to a related class o
 f nonlocal equations. This talk is based on joint works with Jamil Chaker 
 and Minhyun Kim.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Borowski (University of Warsaw)
DTSTART:20221110T144000Z
DTEND:20221110T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/68/">Boundedness of Wolff-type potentials</a>\nby Michał Borowski (Uni
 versity of Warsaw) as part of Function spaces\n\n\nAbstract\nWe study the 
 boundedness of nonlinear operators of Wolff-type in a generalized version.
  The main result is an optimal inequality on the rearrangement of mentione
 d operators\, which allows us to formulate the reduction principle of boun
 dedness between quasi-normed rearrangement invariant spaces into a one-dim
 ensional Hardy-type inequality. The principle can be extended to handle mo
 dulars instead of norms. As Wolff-type potentials are known to control wea
 k solutions to a broad class of quasilinear elliptic PDEs\, we infer regul
 arity properties of the solutions to appropriate problems. The talk is bas
 ed on joint work with Iwona Chlebicka and Błażej Miasojedow.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vjekoslav Kovač (University of Zagreb)
DTSTART:20221020T134000Z
DTEND:20221020T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/69/">Bilinear and trilinear embeddings for complex elliptic operators</
 a>\nby Vjekoslav Kovač (University of Zagreb) as part of Function spaces\
 n\n\nAbstract\nWe will discuss bi(sub)linear and tri(sub)linear embeddings
  for semigroups generated by non-smooth complex-coefficient elliptic opera
 tors in divergence form. Bilinear embeddings can be thought of as sharpeni
 ngs and generalizations of estimates for second-order singular integrals. 
 In the context of complex elliptic operators such $L^p$ bounds were shown 
 by Carbonaro and Dragičević\, who emphasized and crucially used certain 
 generalized convexity properties of powers. We remove this obstruction and
  generalize their approach to the level of Orlicz-space norms that only 
 “behave like powers”. Next\, what we call a trilinear embedding is a p
 araproduct-type estimate. It incorporates bounds for the conical square fu
 nction and finds an application to fractional Leibniz-type rules. In the p
 roofs we use two carefully constructed auxiliary functions that generalize
  a classic Bellman function constructed by Nazarov and Treil in two differ
 ent ways. The talk is based on joint work with Andrea Carbonaro\, Oliver D
 ragičević\, and Kristina Škreb.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Odí Soler i Gibert (University of Würzburg)
DTSTART:20221103T144000Z
DTEND:20221103T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/70/">Dyadic multiparameter $\\mathrm{BMO}$ spaces</a>\nby Odí Soler i 
 Gibert (University of Würzburg) as part of Function spaces\n\n\nAbstract\
 nWe will review some properties of the classical $\\mathrm{BMO}$ space. In
  particular\, we will focus on commutators of the form $[H\,b]\,$ where $b
 $ stands for multiplication by function $b$ in $\\mathrm{BMO}$ and $H$ is 
 the Hilbert transform\, and the equivalence between the norm of $[H\,b]$ (
 as an operator in $\\mathrm{L}^2$) and the $\\mathrm{BMO}$ norm of $b.$ Th
 en\, we will discuss similar results in various generalisations of BMO: we
 ighted spaces and multiparameter spaces. Lastly\, we will present the corr
 esponding dyadic spaces and how to obtain analogous results in this settin
 g. This talk is based on joint works with Komla Domelevo\, Spyridon Kakaro
 umpas and Stefanie Petermichl.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Parissis (University of the Basque Country)
DTSTART:20221124T144000Z
DTEND:20221124T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/71/">Directional averages in codimension one</a>\nby Ioannis Parissis (
 University of the Basque Country) as part of Function spaces\n\n\nAbstract
 \nI will give a brief overview of the theory of directional maximal and si
 ngular averages and describe the connection to the Kakeya/Nikodym line of 
 problems. For general ambient dimension n I will then discuss a sharp L^2-
 bound for d-dimensional averages and codimension n-d=1\, together with con
 sequences for directional square functions of Rubio de Francia type. If ti
 me permits I will mention sharp L^2-bounds for general codimension and a c
 orresponding (d\,n)-Nikodym conjecture.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Nieraeth (Basque Center for Applied Mathematics)
DTSTART:20221215T144000Z
DTEND:20221215T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/72/">Extrapolation in quasi-Banach function spaces</a>\nby Zoe Nieraeth
  (Basque Center for Applied Mathematics) as part of Function spaces\n\n\nA
 bstract\nRubio de Francia's extrapolation theorem allows one to show that 
 an operator that is bounded on weighted Lebesgue spaces for a single expon
 ent and with respect to all weights in the associated Muckenhoupt class ha
 s to also be bounded for every exponent. As a matter of fact\, in the prev
 ious years it has been shown that the operator has to be bounded on a much
  larger class of spaces\, including Lorentz\, variable Lebesgue\, and Morr
 ey spaces\, and further weighted Banach function spaces. In this talk I wi
 ll discuss a recently obtained unification and extension of some of these 
 results by presenting an extrapolation theorem in the setting of general q
 uasi-Banach function spaces\, including limited range and off-diagonal var
 iants.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bae Jun Park (Sungkyunkwan University)
DTSTART:20221222T144000Z
DTEND:20221222T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/73/">Equivalences of (quasi-)norms in a certain vector-valued function 
 space and its applications to multilinear operators</a>\nby Bae Jun Park (
 Sungkyunkwan University) as part of Function spaces\n\n\nAbstract\nIn this
  talk we will study some  (quasi-)norm equivalences\, involving $L^p(\\ell
 ^q)$ norm\, in a certain vector-valued function space and extend the equiv
 alences to $p=\\infty$ and $0 < q < \\infty$ in the scale of Triebel-Lizor
 kin spaces. As an immediate consequence of our results\, $\\Vert f\\Vert_{
 BMO}$ can be written as $L^{\\infty}(\\ell^2)$ norm of a variant of $f$.\n
 We will also discuss some applications to  multilinear operators.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Błażej Wróbel (University of Wrocław)
DTSTART:20230504T134000Z
DTEND:20230504T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/74/">Dimension-free $L^p$ estimates for the vector of maximal Riesz tra
 nsforms</a>\nby Błażej Wróbel (University of Wrocław) as part of Funct
 ion spaces\n\n\nAbstract\nIn 1983 E. M. Stein proved that the vector of cl
 assical Riesz transforms has $L^p$ bounds on $\\mathbb R^d$ which are inde
 pendent of the dimension. I will discuss an analogous result for the vecto
 r of maximal Riesz transforms. I will also mention generalizations to high
 er order Riesz transforms. The talk is based on recent joint work with Mac
 iej Kucharski and Jacek Zienkiewicz (Wrocław).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cody B. Stockdale (Clemson University)
DTSTART:20230216T144000Z
DTEND:20230216T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/75/">A different approach to endpoint weak-type estimates for Calderón
 -Zygmund operators</a>\nby Cody B. Stockdale (Clemson University) as part 
 of Function spaces\n\n\nAbstract\nThe weak-type (1\,1) estimate for Calder
 ón-Zygmund operators is fundamental in harmonic analysis. We investigate 
 weak-type inequalities for Calderón-Zygmund singular integral operators u
 sing the Calderón-Zygmund decomposition and ideas inspired by Nazarov\, T
 reil\, and Volberg. We discuss applications of these techniques in the Euc
 lidean setting\, in weighted settings\, for multilinear operators\, for op
 erators with weakened smoothness assumptions\, and in studying the dimensi
 onal dependence of the Riesz transforms.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tainara Borges (Brown University)
DTSTART:20230316T144000Z
DTEND:20230316T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/76
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/76/">$L^p$ improving continuity estimates and sparse bounds for the bil
 inear spherical maximal function</a>\nby Tainara Borges (Brown University)
  as part of Function spaces\n\n\nAbstract\nIn this talk\, I will explain t
 he interplay between the sharp range of\nparameters for each one has spars
 e domination for certain spherical maximal\nfunctions and the sharp $L^p$\
 nimproving boundedness region of corresponding\nlocalized spherical maxima
 l operators\, an idea that was first exploited in a\nwork of M. Lacey. I w
 ill then talk about joint work with B. Foster\, Y. Ou\,\nJ. Pipher\, and Z
 . Zhou\, in which we proved sparse domination results for a\nbilinear gene
 ralization of the spherical maximal function in any dimension\n$d \\geq 2$
 \, and in dimension $1$ for its lacunary version. Such sparse domination\n
 results allow one to recover the known sharp $L^p \\times L^q \\rightarrow
  L^r$ bounds for the\nbilinear spherical maximal operator and to deduce ne
 w quantitative weighted\nnorm inequalities with respect to bilinear Mucken
 houpt weights.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luz Roncal (BCAM Bilbao)
DTSTART:20230223T144000Z
DTEND:20230223T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/77/">Singular integrals along variable codimension one subspaces</a>\nb
 y Luz Roncal (BCAM Bilbao) as part of Function spaces\n\n\nAbstract\nIn th
 is talk we will consider maximal operators on $\\mathbb{R}^n$ formed by ta
 king arbitrary rotations of tensor products of a $n-1$-dimensional Hörman
 der--Mihlin multiplier with the identity in 1 coordinate. These maximal op
 erators are naturally connected to differentiation problems and maximally 
 modulated singular integrals such as Sjölin's generalization of Carleson'
 s maximal operator. Our main result is a weak-type $L^{2}(\\mathbb{R}^n)$-
 estimate  on band-limited functions. As corollaries\, we obtain: \n\n1. A 
 sharp $L^2(\\mathbb{R}^n)$ estimate for the maximal operator restricted to
  a finite set of rotations in terms of the cardinality of the finite set. 
 \n\n2. A version of the Carleson-Sjölin theorem. \n\nIn addition\, we obt
 ain that functions in the Besov space $B_{p\,1}^0(\\mathbb{R}^n)$\, $2\\le
  p <\\infty$\, may be recovered from their averages along a measurable cho
 ice of codimension $1$ subspaces\, a form of the so-called Zygmund's conje
 cture in general dimension $n$.\n\nThis is joint work with Odysseas Bakas\
 , Francesco Di Plinio\, and Ioannis Parissis.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Nowak (Bielefeld University)
DTSTART:20230302T144000Z
DTEND:20230302T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/78/">Nonlocal gradient potential estimates</a>\nby Simon Nowak (Bielefe
 ld University) as part of Function spaces\n\n\nAbstract\nWe consider nonlo
 cal equations of order larger than one with measure data and present point
 wise bounds of the gradient in terms of Riesz potentials. These gradient p
 otential estimates lead to fine regularity results in many commonly used f
 unction spaces\, in the sense that "passing through potentials" enables us
  to detect finer scales that are difficult to reach by more traditional me
 thods.\nThe talk is based on joint work with Tuomo Kuusi and Yannick Sire.
 \n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armin Schikorra (University of Pittsburgh)
DTSTART:20230323T144000Z
DTEND:20230323T154000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/79/">A Harmonic Analysis perspective on $W^{s\,p}$ as $s \\to 1^-$</a>\
 nby Armin Schikorra (University of Pittsburgh) as part of Function spaces\
 n\n\nAbstract\nWe revisit the Bourgain-Brezis-Mironescu result that the\nG
 agliardo-Norm of the fractional Sobolev space W^{s\,p}\, up to\nrescaling\
 , converges to W^{1\,p} as s\\to 1.\nWe do so from the perspective of Trie
 bel-Lizorkin spaces\, by finding\nsharp $s$-dependencies for several embed
 dings between $W^{s\,p}$ and\n$F^{s\,p}_q$ where $q$ is either 2 or $p$.\n
 We recover known results\, find a few new estimates\, and discuss some\nop
 en questions.\nJoint work with Denis Brazke\, Po-Lam Yung.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olli Saari (Universitat Politècnica de Catalunya)
DTSTART:20230406T134000Z
DTEND:20230406T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/80
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/80/">Construction of a phase space localizing operator</a>\nby Olli Saa
 ri (Universitat Politècnica de Catalunya) as part of Function spaces\n\n\
 nAbstract\nA partition into tiles of the area covered by a convex tree in 
 the Walsh phase plane gives an orthonormal basis for a subspace of L2. The
 re exists a related projection operator\, which has been an important tool
  for dyadic models of the bilinear Hilbert transform. Extending such an ap
 proach to the Fourier model is strictly speaking not possible\, but satisf
 actory substitutes can be constructed. This approach was pursued by Muscal
 u\, Tao and Thiele (2002) for proving uniform bounds for multilinear singu
 lar integrals with modulation symmetry in dimension one. I discuss a multi
 dimensional variant of the problem. This is based on joint work with Marco
  Fraccaroli and Christoph Thiele.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Olivo (ICTP Trieste)
DTSTART:20230413T134000Z
DTEND:20230413T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/81/">About the decay of the Fourier transform of self-similar measures 
 on the complex plane</a>\nby Andrea Olivo (ICTP Trieste) as part of Functi
 on spaces\n\n\nAbstract\nIn this talk we are going to discuss about the be
 haviour of self-similar\nmeasures and its Fourier transform. It is known t
 hat\, in some particular\ncases\, the Fourier transform of a self-similar 
 measure does not go zero\nwhen the frequencies goes to infinity. Neverthel
 ess\, Kaufman and Tsujii\nproved that the Fourier transform of self-simila
 r measures on the real\nline has a power decay outside of a sparse set of 
 frequencies. We will go\nover these results and present a version for homo
 geneous self-similar\nmeasures on the complex plane.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolin Kreisbeck (KU Eichstätt-Ingolstadt)
DTSTART:20230427T134000Z
DTEND:20230427T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/82/">A variational theory for integral functionals involving finite-hor
 izon fractional gradients</a>\nby Carolin Kreisbeck (KU Eichstätt-Ingolst
 adt) as part of Function spaces\n\n\nAbstract\nMotivated by new nonlocal m
 odels in hyperelasticity\, we discuss a class of variational problems with
  integral functionals depending on nonlocal gradients that correspond to t
 runcated versions of the Riesz fractional gradient. We address several asp
 ects regarding the existence theory of these problems and their asymptotic
  behavior. Our analysis relies on suitable translation operators that allo
 w us to switch between the three types of gradients: classical\, fractiona
 l\, and nonlocal. These provide helpful technical tools for transferring r
 esults from one setting to the other. Based on this approach\, we show tha
 t quasiconvexity\, the natural convexity notion in the classical calculus 
 of variations\, characterises the weak lower semicontinuity also in the fr
 actional and nonlocal setting. As a consequence of a general Gamma-converg
 ence statement\, we derive relaxation and homogenization results. The anal
 ysis of the limiting behavior as the fractional order tends to 1 yields lo
 calization to a classical model. This is joint work with Javier Cueto (Uni
 versity of Nebraska-Lincoln) and Hidde Schönberger (KU Eichstätt-Ingolst
 adt).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Irving (Technical University of Dortmund)
DTSTART:20230330T134000Z
DTEND:20230330T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/83/">Fractional differentiability and (p\,q)-growth</a>\nby Christopher
  Irving (Technical University of Dortmund) as part of Function spaces\n\n\
 nAbstract\nI will discuss some recent regularity results obtained for mini
 misers of non-autonomous variational integrals\, with an emphasis towards 
 boundary regularity. We will consider integrands which are non-uniformly e
 lliptic in the sense that they satisfy a natural $(p\,q)$-growth condition
 \, and we will seek improved differentiability in fractional scales. The m
 ain ideas will be illustrated in the interior case\, and some extensions t
 o the boundary will be discussed. The results presented have been obtained
  jointly with Lukas Koch (MPI Lepzig).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasios Fragkos (Washington University in St. Louis)
DTSTART:20230420T134000Z
DTEND:20230420T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/84/">Modulation Invariant Operators near $L^1$</a>\nby Anastasios Fragk
 os (Washington University in St. Louis) as part of Function spaces\n\n\nAb
 stract\nWe prove that the weak-$L^{p}$ norms\, and in fact the sparse $(p\
 ,1)$-norms\, of the Carleson maximal partial Fourier sum operator are $\\l
 esssim (p-1)^{-1}$ as $p\\to 1^+$. Furthermore\, our sparse $(p\,1)$-norms
  bound imply new and stronger results at the endpoint $p=1$. In particular
 \, we obtain that the Fourier series of functions from the weighted Arias 
 de Reyna space $ \\mathrm{QA}_{\\infty}(w) $\, which contains the weighted
  Antonov space $L\\log L\\log\\log\\log L(\\mathbb T\; w)$\, converge almo
 st everywhere whenever $w\\in A_1$. This is an extension of the results of
  Antonov and Arias De Reyna\, where $w$ must be Lebesgue measure.\n\nThe c
 enter of our approach is a sharply quantified near-$L^1$ Carleson embeddin
 g theorem for the modulation-invariant wave packet transform. The proof of
  the Carleson embedding is based on a newly developed smooth multi-frequen
 cy decomposition which\, near the endpoint $p=1$\, outperforms the abstrac
 t Hilbert space approach of past works\, including the seminal one by Naza
 rov\, Oberlin and Thiele. This talk is based on joint work with Francesco 
 Di Plinio.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Weigt (University of Warwick)
DTSTART:20230518T134000Z
DTEND:20230518T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/85
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/85/">Endpoint regularity bounds of maximal operators in higher dimensio
 ns</a>\nby Julian Weigt (University of Warwick) as part of Function spaces
 \n\n\nAbstract\nWe prove the endpoint regularity bound that the variation 
 of various maximal functions is bounded by a constant times the variation 
 of the function in any dimension.\n\nThe key arguments of the proofs are o
 f geometric nature. For example new variants of the isoperimetric inequali
 ty and of the Vitali covering lemma are proven and used. All proofs are mo
 stly elementary up to applications of classical results like the relative 
 isoperimetric inequality and the coarea formula and approximation schemes.
 \n\nSome of the arguments only work for cubes and not for balls. Thus\, fo
 r the uncentered Hardy-Littlewood maximal operator we can only prove the a
 bove endpoint Sobolev bound in the case of characteristic functions. Howev
 er\, we are able to prove it for general functions for example for the max
 imal operator that averages over uncentered cubes with any orientation ins
 tead of balls. The methods also enable a proof of the corresponding endpoi
 nt bound Sobolev for the fractional centered and uncentered Hardy-Littlewo
 od maximal functions.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Sauer (Friedrich Schiller University Jena)
DTSTART:20230511T134000Z
DTEND:20230511T144000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/86/">General Time-Periodic Boundary Value Problems in Weighted Spaces</
 a>\nby Jonas Sauer (Friedrich Schiller University Jena) as part of Functio
 n spaces\n\n\nAbstract\nInbetween elliptic PDEs\, which do not depend on t
 ime (think of the steady-state Stokes equations)\,\nand honest parabolic P
 DEs\, which do depend on time and are started at a given initial value (th
 ink\nof the instationary Stokes equations)\, there are time-periodic parab
 olic PDEs: On the one hand\,\ntime-independent solutions to the elliptic P
 DE are also trivially time-periodic\, which gives periodic\nproblems an el
 liptic touch\, on the other hand solutions to the initial value problem wh
 ich are not\nconstant in time might very well be periodic.\n\nI want to ad
 vocate for time-periodic problems not being the little sister of either el
 liptic or\nparabolic problems\, but being a connector between the two and 
 a class of its own right. This is\nhighlighted by a direct method for show
 ing a priori $L^p$\nestimates for time-periodic\, linear\, partial\ndiffer
 ential equations. The method is generic and can be applied to a wide range
  of problems\, for\nexample the Stokes equations and boundary value proble
 ms of Agmon-Douglas-Nirenberg type. In\nthe talk\, I will present these id
 eas and show how they can be extended to the setting of weighted\n$L^p$\ne
 stimates\, which is advantageous for extrapolation techniques and rougher 
 boundary data.\n\nParts of the talk are based on joint works with Yasunori
  Maekawa and Mads Kyed.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jehoon Ok (Sogang University\, South Korea)
DTSTART:20231024T120000Z
DTEND:20231024T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/87/">Everywhere and partial regularity for parabolic systems with gener
 al growth</a>\nby Jehoon Ok (Sogang University\, South Korea) as part of F
 unction spaces\n\n\nAbstract\nWe discuss on regularity theory for paraboli
 c systems of the form\n\n$$\n\nu_t - \\mathrm{div} A(Du) =0 \\quad \\text{
 in }\\ \\Omega_T=\\Omega\\times(0\,T]\,\n\n$$\n\nwhere $u:\\Omega_T\\to \\
 mathbb{R}^N$\, $u=u(x\,t)$\, is a vector valued function and the nonlinear
 ity $A:\\mathbb{R}^{nN}\\to \\mathbb{R}^{nN}$ satisfies a general Orlicz g
 rowth condition characterized by exponents $p$ and $q$\, subject to the in
 equality $\\frac{2n}{n+2}<p<q$. It is noteworthy that when if $p<2<q$\, th
 e degeneracy of the system remains indeterminate. \n\n\n\nThis talk focuse
 s on presenting my recent developments in the realm of regularity results 
 concerning  the spatial gradient $Du$ of solutions of the above system\, w
 hich include the higher higher integrability of $Du$\, H\\"older continuit
 y of $Du$ when $A(\\xi)$ satisfies the Uhlenbeck structure\, i.e.\, $A(\\x
 i)=\\frac{\\varphi'(|\\xi|)}{|\\xi|}\\xi$\, and partial H\\"older continui
 ty of $Du$. These results are joint works with Giovanni Scilla and Bianca 
 Stroffolini from University of Naples\, Federico II\, and Peter H\\"ast\\"
 o from University of Turku.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Weimar (Die Julius-Maximilians-Universität Würzburg)
DTSTART:20231010T120000Z
DTEND:20231010T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/88/">Theory of Function Spaces: On Classical Tools for Modern Spaces</a
 >\nby Markus Weimar (Die Julius-Maximilians-Universität Würzburg) as par
 t of Function spaces\n\n\nAbstract\nIn the first part of this talk\, we di
 scuss basic principles of the theory of function spaces. In particular\, w
 e briefly recall the Fourier analytical approach towards classical smoothn
 ess spaces of distributions and point out their importance in the areas of
  approximation theory and the regularity theory of PDEs.\n\nThe main part 
 of the talk is devoted to so-called Triebel-Lizorkin-Morrey spaces $\\math
 cal{E}_{u\,p\,q}^s$ of positive smoothness $s$ which attracted some attent
 ion in the last 15 years. This family of function spaces generalizes the b
 y now well-established scale of Triebel-Lizorkin spaces $F^s_{p\,q}$ which
  particularly contains the usual $L_p$-Sobolev spaces $H^s_p=F^s_{p\,2}$ a
 s special cases. Moreover\, there are strong relations to standard classes
  of functions like BMO and Campanato spaces which are widely used in the a
 nalysis of PDEs.\nWe will present new characterizations of Triebel-Lizorki
 n-Morrey spaces in terms of classical tools such as local oscillations (i.
 e.\, local polynomial bestapproximations) as well as ball means of higher 
 order differences. Hence\, under standard assumptions on the parameters in
 volved\, we extend assertions due to Triebel 1992 and Yuan/Sickel/Yang 201
 0 for spaces $\\mathcal{E}_{u\,p\,q}^s$ on $\\mathbb{R}^d$ and additionall
 y consider their restrictions to (bounded) Lipschitz domains $\\Omega\\sub
 seteq \\mathbb{R}^d$. \nIf time permits\, we moreover indicate possible ap
 plications to the regularity theory of quasi-linear elliptic PDEs. \nThe r
 esults to be presented are based on a recent preprint [1] in joint work wi
 th Marc Hovemann (Marburg).\n\n[1] M.~Hovemann and M.~Weimar. Oscillations
  and differences in Triebel-Lizorkin-Morrey spaces. Submitted preprint (ar
 Xiv:2306.15239)\, 2023.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor I. Skrypnik (Institute Applied Mathematics and Mechanics of t
 he NAS Ukraine)
DTSTART:20231205T130000Z
DTEND:20231205T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/89
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/89/">Some remarks on the weak Harnack  inequality for unbounded minimiz
 ers of elliptic functionals with  generalized Orlicz growth</a>\nby Igor I
 . Skrypnik (Institute Applied Mathematics and Mechanics of the NAS Ukraine
 ) as part of Function spaces\n\n\nAbstract\nWe prove the weak Harnack type
  inequalities for nonnegative unbounded minimizers of  corresponding ellip
 tic functionals under the non-logarithmic \nZhikov's conditions\, roughly 
 speaking we consider the following De Giorgi's classes\n$$\n\\int\\limits_
 {B_{(1-\\sigma)r}(x_{0})}\\varPhi\\Big(x\,|(u-k)_{-}|\\Big)\\\,dx \\leqsla
 nt \\gamma \\int\\limits_{B_{r}(x_{0})}\\varPhi\\Big(x\,\\frac{(u-k)_{-}}{
 \\sigma r}\\Big)\\\,dx\,\n$$\n$\\sigma$\, $r\\in(0\,1)$\, $k>0$ and $\\var
 Phi(x\,\\cdot)$ satisfies the so-called ($p\,q$)-growth conditions. We are
  interesting in the case when \n$\\gamma$ depends on $r$\, it turns out th
 at in this case it is impossible to use standard classical techniques. Our
  results cover new cases of  double-phase\, degenerate double-phase functi
 onals\, non uniformly elliptic functionals  and functionals with variable 
 exponents.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emiel Lorist (Delft University of Technology)
DTSTART:20231219T130000Z
DTEND:20231219T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/90
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/90/">A discrete framework for the interpolation of Banach spaces</a>\nb
 y Emiel Lorist (Delft University of Technology) as part of Function spaces
 \n\n\nAbstract\nInterpolation of bounded linear operators on Banach spaces
  is a widely used technique in analysis. Key roles are played by the real 
 and complex interpolation methods\, but there is also a wealth of other in
 terpolation methods\, for example relevant in the study of (S)PDE. In this
  talk I will introduce interpolation of Banach spaces using a new\, discre
 te framework. I will discuss how this framework extends and unifies variou
 s results in the literature. Moreover\, I will discuss its applications to
  parabolic boundary value problems.\nThis talk is based on joint work with
  Nick Lindemulder (Radboud University Nijmegen).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Duncan (ICMAT Madrid)
DTSTART:20231121T130000Z
DTEND:20231121T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/91/">Brascamp-Lieb Inequalities: Their Theory and Some Applications</a>
 \nby Jennifer Duncan (ICMAT Madrid) as part of Function spaces\n\n\nAbstra
 ct\nThe Brascamp-Lieb inequalities form a class of multilinear inequalitie
 s that includes a variety of well-known classical results\, such as Hölde
 r’s inequality\, Young’s convolution inequality\, and the Loomis-Whitn
 ey inequality\, for example. Their theory is surprisingly multifaceted\, i
 nvolving ideas from semigroup interpolation\, convex optimisation\, and ab
 stract algebra. In the first half of this talk\, we will discuss some of t
 he key aspects of this theory and some important variants on the Brascamp-
 Lieb framework\; in the second half\, we will talk specifically about how 
 these inequalities arise in harmonic analysis\, in particular about their 
 use in fourier restriction theory and in recent results on the boundedness
  of the helical maximal function. If time permits\, we will then talk abou
 t some more far-reaching connections with other areas of mathematics and t
 he sciences.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnendu Sil (Indian Institute of Science Bengaluru)
DTSTART:20231107T130000Z
DTEND:20231107T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/92/">BMO estimates for Hodge-Maxwell systems with discontinuous anisotr
 opic coefficients</a>\nby Swarnendu Sil (Indian Institute of Science Benga
 luru) as part of Function spaces\n\n\nAbstract\nThe time-harmonic Maxwell 
 system in a bounded domain is \n		$$\n	\\left\\lbrace \\begin{aligned}\n		
 	curl  H  &=  i\\omega \\varepsilon \\left(x\\right) E + J_{e}    \n				&&
 \\text{ in } \\Omega\, \\\\\n				\\operatorname*{curl} E &= -i\\omega \\mu
 \\left(x\\right) H + J_{m}     &&\\text{ in } \\Omega\, \\\\\n				\\nu \\t
 imes E &= \\nu \\times E_{0} &&\\text{  on } \\partial\\Omega\,\n			\\end{
 aligned} \n			\\right.\n		$$\n		where $E\, H$ are unknown vector fields\, 
 $E_{0}\, J_{e}\, J_{m}$ are given vector fields and $\\varepsilon\, \\mu$ 
 are given $3\\times 3$ matrix fields which are bounded\, measurable and un
 iformly elliptic. When $\\varepsilon\, \\mu$ have sufficient regularity\, 
 e.g. Lipschitz\, then one can show that $(E\, H)$ inherits the same regula
 rity as $(J_{e}\, J_{m})$\, as long as $E_{0}$ is as regular. \n		\n		\\pa
 r In this talk\, we shall discuss the sharpest regularity assumptions on $
 \\varepsilon\, \\mu$ under which $(E\, H)$ inherits BMO regularity from $(
 J_{e}\, J_{m}).$  As it turns out\, the minimal regularity assumption on $
 \\varepsilon\, \\mu$ is that their components belong to a class of `small 
 multipliers of BMO'. This class neither contains nor is contained in $C^{0
 }.$ Thus our results prove the validity of BMO estimates for a class of di
 scontinuous coefficients. Our results are actually holds more generally\, 
 for systems of differential $k$-forms of similar type in any dimension $n 
 \\geq 3.$ \n		\n		\\par This is a joint work with my post-doctoral student
  Dharmendra Kumar.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kim  Myyryläinen (Aalto University)
DTSTART:20240220T130000Z
DTEND:20240220T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/93/">Parabolic Muckenhoupt weights</a>\nby Kim  Myyryläinen (Aalto Uni
 versity) as part of Function spaces\n\n\nAbstract\nWe discuss parabolic Mu
 ckenhoupt weights related to a doubly nonlinear parabolic partial differen
 tial equation (PDE). In the natural geometry of the PDE\, the time variabl
 e scales to the power in the structural conditions for the PDE. Consequent
 ly\, the Euclidean balls and cubes are replaced by parabolic rectangles re
 specting this scaling in all estimates. The main challenge is that in the 
 definition of parabolic Muckenhoupt weights one of the integral averages i
 s evaluated in the past and the other one in the future with a time lag be
 tween the averages. Another main motivation is that the parabolic theory i
 s a higher dimensional version of the one-sided setting and the correspond
 ing one-sided maximal function.\nThe main results include a characterizati
 on of weak and strong type weighted norm inequalities for forward in time 
 parabolic maximal functions and parabolic versions of the Jones factorizat
 ion and the Coifman--Rochberg characterization. In addition to parabolic M
 uckenhoupt weights\, the class of parabolic $A_\\infty$ weights is discuss
 ed from the perspective of parabolic reverse H\\"older inequalities. We co
 nsider several characterizations and self-improving properties for this cl
 ass of weights and study their connection to parabolic Muckenhoupt conditi
 ons. A sufficient condition is given for the implication from parabolic re
 verse Holder classes to parabolic Muckenhoupt classes.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Brasco (Università degli Studi di Ferrara)
DTSTART:20240319T130000Z
DTEND:20240319T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/94
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/94/">Around Hardy's inequality for convex sets</a>\nby Lorenzo Brasco (
 Università degli Studi di Ferrara) as part of Function spaces\n\n\nAbstra
 ct\nWe start by reviewing the classical Hardy inequality for convex sets.\
 nWe then discuss the counterpart of Hardy's inequality for the case of fra
 ctional Sobolev-Slobodecki\\u{\\i} spaces\, still in the case of open conv
 ex subsets of the Euclidean space. In particular\, we determine the sharp 
 constant in this inequality\, by constructing explicit supersolutions base
 d on the distance function.\nWe also show that this method works only for 
 the {\\it mildly nonlocal} regime and it is bound to fail for the {\\it st
 rongly nonlocal} one. We conclude by presenting some open problems.\n\\par
 \nSome of the results presented are issued from papers in collaboration wi
 th Francesca Bianchi (Ferrara \\& Parma)\, Eleonora Cinti (Bologna)\, Firo
 j Sk (Oldenburg) and Anna Chiara Zagati (Ferrara \\& Parma).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Firoj Sk (University of Oldenburg)
DTSTART:20240402T120000Z
DTEND:20240402T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/95
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/95/">On Morrey's inequality in fractional Sobolev spaces.</a>\nby Firoj
  Sk (University of Oldenburg) as part of Function spaces\n\n\nAbstract\nWe
  study the sharp constant in Morrey's inequality for fractional Sobolev sp
 aces on the entire Euclidean space of dimension N\, when 0<s<1 and p>1 are
  such that sp>N. In a series of recent articles by Hynd and Seuffert\, we 
 discuss the existence of the Morrrey extremals together with some regulari
 ty results. We analyse the sharp asymptotic behaviour of the Morrey consta
 nt in the following cases:\n\ni) when N\, p are fixed with N<p\, and s go 
 to N/p\,\n\nii) when s\, N are fixed\, and p tends to infinity\,\n\niii) w
 hen N\, p are fixed with N<p\, and s goes to 1. \n\nWe further demonstrate
  the convergence of extremals as s goes to 1\, which ensures the consisten
 cy of the well-known local results by Hynd and Seuffert. This talk is base
 d on joint works with L. Brasco and F. Prinari.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémy Rodiac (University of Warsaw)
DTSTART:20240305T130000Z
DTEND:20240305T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/96
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/96/">A relaxation approach for the minimisation of the neo-Hookean ener
 gy</a>\nby Rémy Rodiac (University of Warsaw) as part of Function spaces\
 n\n\nAbstract\nThe neo-Hookean model is a famous model for elastic materia
 ls. However it is still not known if the neo-Hookean energy admits a minim
 iser in an appropriate function space in 3D. I will explain what is the di
 fficulty one encounters when we try to apply the direct method of calculus
  of variations to this problem: this is the lack of compactness of the min
 imisation space. I will also present a relaxation approach whose aim is to
  transform the problem of lack of compactness into a problem of regularity
  for a modified problem. The talk will be based on joint works with M. Bar
 chiesi\, C. Mora-Corral and D. Henao.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil Airta (University of Málaga)
DTSTART:20240416T120000Z
DTEND:20240416T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/97
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/97/">Singular integrals: Multiparameter framework and Zygmund dilation<
 /a>\nby Emil Airta (University of Málaga) as part of Function spaces\n\n\
 nAbstract\nOver a half-century ago\, Alberto Calderón and Antoni Zygmund 
 made groundbreaking studies that initiated the study of modern harmonic an
 alysis that focuses on singular integrals.\nThese operators still lie at t
 he core of today's harmonic analysis.\nRecently\, studies of singular inte
 grals have been fast-paced due to new techniques that are based on similar
  underlying methods as in the classical studies by Calderón and Zygmund.\
 nThese new techniques\, namely the sparse method and the representation th
 eory\, have enabled us to find\, for example\, sharp weighted estimates an
 d handle more complex operators such as multiparameter singular integrals.
 \nMultiparameter framework refers to the study of singular integrals whose
  singularity is more delicate to work with as it is expanded over the unde
 rlying space.\nIn this talk\, I will be giving an introduction to the stud
 y of singular integrals and extensions to the multiparameter framework\, w
 here we will be focusing\, especially on the kernels that are dilation inv
 ariant under a specific "entangled" dilation - the so-called Zygmund dilat
 ion.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentina Ciccone (University of Bonn)
DTSTART:20240430T120000Z
DTEND:20240430T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/98
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/98/">Endpoint estimates for higher-order Marcinkiewicz multipliers</a>\
 nby Valentina Ciccone (University of Bonn) as part of Function spaces\n\n\
 nAbstract\nMarcinkiewicz multipliers on the real line are bounded function
 s of uniformly bounded variation \non each Littlewood-Paley dyadic interva
 l.  \nThe corresponding multiplier operators are well known to be bounded 
 on $L^p(\\mathbb{R})$ for all $1< p< \\infty$. Optimal weak-type endpoint 
 estimates for these operators have been studied by Tao and Wright who prov
 ed that \nthey map locally $L\\log^{1/2}L$ to weak $L^1$.\n\nIn this talk\
 , we consider higher-order Marcinkiewicz multipliers\, that is multipliers
  of uniformly bounded variation on each interval arising from a higher-ord
 er lacunary partition of the real line. We discuss optimal weak-type endpo
 int estimates for the corresponding multiplier operators. \nThese are esta
 blished as a consequence of a more general endpoint result \nfor a higher-
 order variant of a class of multipliers introduced by Coifman\, Rubio de F
 rancia\, and Semmes and further studied by Tao and Wright.\n\n\nThe semina
 r is based on joint work with Odysseas Bakas\, Ioannis Parissis\, and Marc
 o Vitturi.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arran Fernandez (Eastern Mediterranean University)
DTSTART:20240423T120000Z
DTEND:20240423T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/99/">Function spaces for fractional integrals and derivatives</a>\nby A
 rran Fernandez (Eastern Mediterranean University) as part of Function spac
 es\n\n\nAbstract\nFractional calculus investigates the generalisation of d
 erivatives and integrals to orders outside of the integers. Unlike classic
 al derivatives and integrals\, fractional-order operators do not have a si
 ngle unique definition\, but many competing formulae which can be categori
 sed into broader families of operators. An immediate concern arising\, whe
 n such operators are defined\, is the question of what spaces they act on 
 and between. This talk will attempt to provide an overview of some of the 
 commonly used function spaces for fractional integrals and derivatives\, w
 ith some discussion of their advantages and disadvantages according to the
  purposes at hand. If time allows\, some discussion of generalised fractio
 nal-calculus operators will also be included\, with notes on whether the s
 ame function spaces can be used or must be modified when we extend from cl
 assical to generalised settings.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Evseev (Okinawa Institute of Science and Technology)
DTSTART:20241001T120000Z
DTEND:20241001T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/100/">Weakly weakly* differentiable functions</a>\nby Nikita Evseev (Ok
 inawa Institute of Science and Technology) as part of Function spaces\n\n\
 nAbstract\nWe discuss various notions of weak differentiability of Banach-
 valued functions. There is the theory of Sobolev spaces of Banach-valued f
 unctions built on the notion of weak derivatives. In most issues\, it repr
 oduces properties from the real-valued case. However\, this approach is no
 t consistent with its metric counterpart. To overcome this\, one would emp
 loy weak weak* derivatives. The properties of the last ones are far beyond
  the scalar case (for instance\, those derivatives need not be unique or m
 easurable). On the other hand\, it allows us to define Sobolev mappings va
 lued in a metric space via isometric embedding of the metric space into a 
 Banach space.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Behn (Bielefeld University)
DTSTART:20241015T120000Z
DTEND:20241015T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/101
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/101/">Nonlocal equations with degenerate weights</a>\nby Linus Behn (Bi
 elefeld University) as part of Function spaces\n\n\nAbstract\nWe give a de
 finition for fractional weighted Sobolev spaces with degenerate\nweights. 
 We provide embeddings and Poincare inequalities for these spaces and\nshow
  robust convergence when the parameter of fractional differentiability goe
 s\nto 1. Moreover\, we prove local H¨older continuity and Harnack inequal
 ities for\nsolutions to the corresponding weighted nonlocal integrodiffere
 ntial equations.\nJoint work with Lars Diening (Bielefeld)\, Jihoon Ok (Se
 oul)\, and Julian Rolfes\n(Bielefeld).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Detaille (Université Claude Bernard Lyon 1)
DTSTART:20241112T130000Z
DTEND:20241112T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/102/">Sobolev mappings to manifolds: when geometric analysis interacts 
 with function spaces</a>\nby Antoine Detaille (Université Claude Bernard 
 Lyon 1) as part of Function spaces\n\n\nAbstract\nIn many applications to 
 problems coming e.g. from physics or\nnumerical methods\, it is natural to
  consider Sobolev mappings that are\nconstrained to take their values into
  a given manifold.\nAlthough being defined as a subset of a classical Sobo
 lev space of\nvector-valued maps\, the Sobolev space of mappings taking th
 eir values\ninto a given manifold may have striking qualitatively differen
 t properties.\nIn this talk\, we will explain some selected problems arisi
 ng in the\nstudy of these manifold-valued Sobolev mappings.\nThe goal will
  be twofold: (1) give an insight on why these problems are\ninteresting an
 d what are the key phenomena at work there\, and (2)\nillustrate how geome
 tric analysis can give incentive to study classical\n(real-valued) functio
 n spaces\, and combine the tools produced in this\nprocess with geometric 
 tools in order to solve challenging problems.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Di Donato (University of Pavia)
DTSTART:20241029T130000Z
DTEND:20241029T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/103
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/103/">Rectifiability in Carnot groups</a>\nby Daniela Di Donato (Univer
 sity of Pavia) as part of Function spaces\n\n\nAbstract\nIntrinsic regular
  surfaces in Carnot groups play the same role as C^1 surfaces in Euclidean
  spaces. As in Euclidean spaces\, intrinsic regular surfaces can be locall
 y defined in different ways: e.g. as non critical level sets or as continu
 ously intrinsic differentiable graphs. The equivalence of these natural de
 finitions is the problem that we are studying. Precisely our aim is to gen
 eralize some results proved by Ambrosio\, Serra Cassano\, Vittone valid in
  Heisenberg groups to the more general setting of Carnot groups. This is j
 oint work with Antonelli\, Don and Le Donne\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Lerner (Bar-Ilan University)
DTSTART:20241203T130000Z
DTEND:20241203T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/104
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/104/">On some quantitative weighted weak type inequalities</a>\nby Andr
 ei Lerner (Bar-Ilan University) as part of Function spaces\n\n\nAbstract\n
 In this talk I will discuss quantitative weighted weak type inequalities o
 f Muckenhoupt--Wheeden type\, both in the matrix and scalar settings.In pa
 rticular\, in the matrix setting we obtain the sharp bound for the Christ-
 -Goldberg maximal operator in the range $p \\in (1\,2)$.Also\, in the scal
 ar setting\,\nwe obtain an improved bound for Calderon--Zygmund operators 
 in the range $p\\in (1\,p^*)$\, where $p^*$ is the root of the cubic equat
 ion $p^3-2p^2+p-1=0$.\n\nThe talk is based on joint work with Kangwei Li\,
  Sheldy Ombrosi and Israel Rivera-Ríos.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duvan Henao (Instituto de Ciencias de la Ingeniería\, Universidad
  de O’Higgins)
DTSTART:20250408T120000Z
DTEND:20250408T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/105/">NeoHookean energies\, cavitation\, and relaxation in nonlinear el
 asticity</a>\nby Duvan Henao (Instituto de Ciencias de la Ingeniería\, Un
 iversidad de O’Higgins) as part of Function spaces\n\n\nAbstract\nThe ne
 oHookean model is one of the most commonly used approaches to study the me
 chanical response of elastic bodies undergoing large deformations. However
 \, the neoHookean energy is expected to possess no minimizers in the Sobol
 ev class naturally associated to its quadratic coercivity. This is connect
 ed to the formation and sudden expansion of voids observed in confined ela
 stomers. There is analytical evidence for the conjecture that the nonexist
 ence is due to the opening of an ever larger number of cavities. Regulariz
 ations of the neoHookean model either impose a length-scale for the caviti
 es created (with a second gradient\, or taking into account the energy req
 uired to stretch the created surface) or impose a bound in the number of c
 avities that the body is allowed to open. In the second approach\, the fir
 st existence results are due to Henao & Rodiac (2018) in the axisymmetric 
 class for hollow domains\, and to Doležalová\, Hencl & Molchanova (2024)
  in the weak closure of homeomorphisms in 3D. In more general classes wher
 e harmonic dipoles are admitted\, a relaxation approach has been proposed 
 by Barchiesi\, Henao\, Mora-Corral & Rodiac (2023\, 2024)\, where the mass
  of the singular part of the derivative of the inverse is found to accurat
 ely give the cost of creating dipole singularities.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Mora-Corral (Universidad Autónoma de Madrid)
DTSTART:20250225T130000Z
DTEND:20250225T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/106
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/106/">Invertibility conditions for Sobolev maps</a>\nby Carlos Mora-Cor
 ral (Universidad Autónoma de Madrid) as part of Function spaces\n\n\nAbst
 ract\nIn nonlinear elasticity\, a deformation is represented by a Sobolev 
 map. In order to be physically acceptable\, the deformation must preserve 
 the orientation and cannot interpenetrate matter. There are several ways t
 o model mathematically these restrictions\, but a popular choice is that t
 he deformation must have positive Jacobian and be injective (almost everyw
 here). The first restriction is local and the second is global. In this ta
 lk I will review some theorems guaranteeing injectivity from the positivit
 y of the Jacobian together with other assumptions. As a consequence\, I wi
 ll present results on the existence of injective minimizers for elastic en
 ergies.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Dragičević (University of Ljubljana)
DTSTART:20250422T120000Z
DTEND:20250422T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/107
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/107/">The $p$-ellipticity condition for systems of partial differential
  equations with complex coefficients</a>\nby Oliver Dragičević (Universi
 ty of Ljubljana) as part of Function spaces\n\n\nAbstract\nWe extend the c
 oncept of $p$-ellipticity for (single) elliptic operators\, that we introd
 uced in 2016\, to the case of systems of elliptic equations with complex c
 oefficients. We prove several key properties of $p$-ellipticity akin to th
 ose that have been known to hold in the scalar case. In some respects\, ho
 wever\, the vector case fundamentally differs from the scalar one.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandros Eskenazis (Sorbonne Université and University of Cambr
 idge)
DTSTART:20250325T130000Z
DTEND:20250325T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/109
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/109/">Discrete logarithmic Sobolev inequalities in Banach spaces</a>\nb
 y Alexandros Eskenazis (Sorbonne Université and University of Cambridge) 
 as part of Function spaces\n\n\nAbstract\nWe shall discuss certain aspects
  of vector-valued harmonic analysis on the discrete hypercube. After prese
 nting classical scalar-valued inequalities going back to Talagrand’s wor
 k in the 1990s\, we will survey recent developments on vector-valued Poinc
 aré inequalities. Then\, we will proceed to present a new optimal vector-
 valued logarithmic Sobolev inequality in this context. The talk is based o
 n joint work with D. Cordero-Erausquin (Sorbonne).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dariusz Kosz (Wroclaw University of Science and Technology)
DTSTART:20250311T130000Z
DTEND:20250311T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/110
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/110/">Variation of the centered maximal function</a>\nby Dariusz Kosz (
 Wroclaw University of Science and Technology) as part of Function spaces\n
 \n\nAbstract\nLet M be the centered Hardy–Littlewood maximal operator on
  the real line. Is it true that the total variation of the maximal functio
 n Mf does not exceed the total variation of f?\n\nIn this talk\, I verify 
 this conjecture for simple functions with zero and nonzero values alternat
 ing. I also discuss a strengthened version of the conjecture and the equiv
 alence of the continuous and discrete settings in this context.\n\nMy talk
  is based on a joint project with Paul Hagelstein and Krzysztof Stempak.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Oikari (University of Helsinki)
DTSTART:20250429T120000Z
DTEND:20250429T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/111
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/111/">Global exponential integrability of parabolic BMO functions</a>\n
 by Tuomas Oikari (University of Helsinki) as part of Function spaces\n\n\n
 Abstract\nA result of Smith and Stegenga from the '90s states that in doma
 ins $\\Omega\\subset\\mathbb{R}^n$ functions of bounded mean oscillation $
 \\mathrm{BMO}(\\Omega) \\subset \\mathrm{EI}(\\Omega)$ are globally expone
 ntially integrable if and only if $\\Omega$ satisfies a quasihyperbolic bo
 undary condition. This is a geometric characterization of an embedding bet
 ween function spaces\, motivated by the global integrability of solutions 
 of elliptic PDEs on domains\, such as the Laplacian.\nFor parabolic PDEs o
 n $\\mathbb{R}^{n}_x\\times\\mathbb{R}_t\,$ such as the parabolic $p$-Lapl
 ace\, the relevant space of interest is the forward-in-time parabolic BMO\
 , a classical work of Moser from the '60s.\nIn this talk I discuss a paral
 lel of the result of Smith and Stegenga in the parabolic context of Moser\
 , where the embedding of interest and the quasihyperbolic boundary conditi
 on both become oriented in time.\n\nThis talk is based on a joint work wit
 h Kim Myyryläinen and Olli Saari.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Björn (Linköping University)
DTSTART:20251125T130000Z
DTEND:20251125T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/112
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/112/">Quasicontinuouity of Newtonian Sobolev functions and outer capaci
 ties based on Banach function spaces</a>\nby Anders Björn (Linköping Uni
 versity) as part of Function spaces\n\n\nAbstract\nThe equivalence classes
  in the (first-order real-valued) Sobolev space\n$W^{1\,p}$ are up to a.e.
 \, but there are better\nrepresentatives.\n\nThe corresponding Newtonian S
 obolev space $N^{1\,p}(\\mathcal{P})$\non a metric space $\\mathcal{P}$ is
  defined\nas those $L^p$ functions that have upper gradients in $L^p$.\nTh
 is \nmakes them automatically better defined than a.e.\, since\nthe bad re
 presentatives lack upper gradients in $L^p$.\n\nIt has been an open proble
 m since the late 1990s whether \nfunctions in $N^{1\,p}(\\mathcal{P})$ are
 \nalways quasicontinuous. \nThe most general results is due to \nEriksson-
 Bique and Poggi-Corradini (2024) who showed this\nwhen $\\mathcal{P}$ is l
 ocally complete.\n\nQuasicontinuity is also closely connected to whether t
 he\nassociated (Sobolev) capacity is an outer capacity.\n\nIn this talk I 
 will take a look at these questions \nif we replace the $L^p$ norm by a mo
 re \ngeneral Banach function space/lattice norm.\nA particular focus will 
 be on $L^\\infty$.\n\nThis is based on joint work with Jana Björn and Luk
 áš Malý.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Odysseas Bakas (University of Patras)
DTSTART:20251007T120000Z
DTEND:20251007T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/113
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/113/">A dyadic approach to the study of products of functions in $H^1$ 
 and $BMO$</a>\nby Odysseas Bakas (University of Patras) as part of Functio
 n spaces\n\n\nAbstract\nIt was shown by A. Bonami\, T. Iwaniec\, P. Jones\
 , and M. Zinsmeister that the product of a function in the Hardy space $H^
 1(\\mathbb{D})$ and a function in $BMOA(\\mathbb{D})$ belongs to the Hardy
 -Orlicz space $H^{\\log}(\\mathbb{D})$\, and that every function in $H^{\\
 log}(\\mathbb{D})$ can be written as such a product.\n\nIn this talk\, we 
 present a dyadic approach to the study of products of functions in $H^1$ a
 nd $BMO$\, as well as to the study of the associated Hardy-Orlicz spaces.\
 n\nThe talk is based on joint work with Sandra Pott\, Salvador Rodríguez-
 López\, and Alan Sola.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Alexis (University of Bonn)
DTSTART:20251111T130000Z
DTEND:20251111T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/114
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/114/">How to represent a function in a quantum computer</a>\nby Michel 
 Alexis (University of Bonn) as part of Function spaces\n\n\nAbstract\nWe d
 efine the SU(2)-valued nonlinear Fourier transform and explain its connect
 ion with quantum signal processing. In particular\, we provide an algorith
 m to compute the inverse nonlinear Fourier transform in a special case\, w
 hich allows one to represent most functions in a quantum computer. Finally
 \, we mention the higher dimensional analog with the SU(2n)-valued nonline
 ar Fourier transform. This talk includes joint work with L. Becker\, L. Li
 n\, G. Mnatsakanyan\, D. Oliveira e Silva\, C. Thiele and J. Wang.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Alberto Antonini (National Institute of High Mathematics (In
 DAM)\, University of Florence\, Italy)
DTSTART:20251021T120000Z
DTEND:20251021T130000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/115
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/115/">Second-order estimates in anisotropic elliptic problems</a>\nby C
 arlo Alberto Antonini (National Institute of High Mathematics (InDAM)\, Un
 iversity of Florence\, Italy) as part of Function spaces\n\n\nAbstract\nIn
  recent years\, various results showed that second-order regularity of  so
 lutions to the $p$-Laplace equation \n$$\n     -\\Delta_p u=-\\mathrm{div}
 \\big(|\\nabla u|^{p-2}\\nabla u \\big)=f\,\\quad p>1\,\n$$\ncan be proper
 ly formulated in terms of the expression under the divergence\, the so-cal
 led stress field\, see [3].\n\n \n I will discuss the extension of these r
 esults to the anisotropic $p$-Laplace problem\, namely equations of the ki
 nd\n$$\n-\\mathrm{div}\\\,\\big(\\mathcal{A}(\\nabla u)\\big)=f\\\,\,\n$$\
 n in which the stress field is given by $\\mathcal{A}(\\nabla u)=H^{p-1}(\
 \nabla u)\\\,\\nabla_\\xi H(\\nabla u)$\, where $H(\\xi)$ is a norm on $\\
 mathbb{R}^n$ satisfying suitable ellipticity assumptions.\n\n$W^{1\,2}$-So
 bolev regularity of $\\mathcal{A}(\\nabla u)$ is established when $f$ is s
 quare integrable\, and both local and global estimates are obtained. The l
 atter apply to solutions to homogeneous Dirichlet problems on sufficiently
  regular domains.\nA key point in our proof is an extension of Reilly's id
 entity to the anisotropic setting.\n\nThis is based on joint works with A.
  Cianchi\, G. Ciraolo\, A.\nFarina and V.G. Maz'ya.\n\n  \n[1]  C.A. Anton
 ini\, G. Ciraolo\, A. Farina\, Interior regularity results for inhomogeneo
 us anisotropic quasilinear equations\, Math. Ann. (2023).\n \n\n[2] C.A. A
 ntonini\, A. Cianchi\, G. Ciraolo\, A. Farina\, V.G. Maz'ya\, Global secon
 d-order estimates in anisotropic elliptic problems\, Proc. Lond. Math. Soc
 . (3)\, vol. 130\, no. 3\, 60 pp.\, (2025)\n\n[3] A. Cianchi\, V.G. Maz'ya
 \, Second-order two-sided estimates in nonlinear elliptic problems\, Arch.
  Ration. Mech. Anal. 229 (2018)\, no. 2\, 569-599.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Georg Feichtinger (University of Vienna)
DTSTART:20251216T130000Z
DTEND:20251216T140000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/116
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/116/">What is a Continuous Orthonormal Basis? How the Ideas used in Phy
 sics can be put on a Sound Mathematical Ground</a>\nby Hans Georg Feichtin
 ger (University of Vienna) as part of Function spaces\n\n\nAbstract\nWhen 
 it comes to the use of the family of Dirac measures on the real line of th
 e Euclidean space R^d physicist and engineers often use weird formulas\, i
 nvolving divergent integrals\, which are often manipulated in a formal way
 \, based on the analogy to the finite discrete case\, where such manipulat
 ions are justified within linear algebra.\n\nThe talk is going to describe
  some ongoing discussion which aims at a mathematically sound description 
 of such formal manipulations in the context of mild distributions. Mild di
 stributions form together with the Hilbert space L2(R^d) and the underlyin
 g Banach algebra S_0(R^d) of test functions (the Feichtinger algebra) a so
 -called Banach Gelfand triple or rigged Hilbert space\, comparable with th
 e Schwartz setting leading to (the much larger space of) tempered distribu
 tions.\n\nUsing this setting the claim that the (continuous) Fourier trans
 form is nothing else but a change of basis\, moving from the Dirac basis t
 o the (equivalent) Fourier basis\, makes sense and can be very well justif
 ied.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iker Gardeazabal Gutiérrez
DTSTART:20260225T094000Z
DTEND:20260225T104000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/117
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/117/">Self-improving properties of generalized Poincaré inequalities</
 a>\nby Iker Gardeazabal Gutiérrez as part of Function spaces\n\n\nAbstrac
 t\nIn this talk\, we will discuss a method to obtain extensions of the cla
 ssical Poincaré-Sobolev inequalities. The main tools of this method are t
 he different forms of self-improving properties that the generalized Poinc
 aré inequalities satisfy. The first part of the talk will focus on these 
 self-improving properties\, including some recent improvements\, while the
  second part will present some applications of this method.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spyridon Kakaroumpas (University of Würzburg)
DTSTART:20260325T094000Z
DTEND:20260325T104000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/118
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/118/">Multilinear singular integral theory for matrix weights</a>\nby S
 pyridon Kakaroumpas (University of Würzburg) as part of Function spaces\n
 \nInteractive livestream: https://cesnet.zoom.us/j/99825599862\n\nAbstract
 \nThe action of classical operators such as maximal functions or the Hilbe
 rt transform on weighted Lebesgue spaces is one of the main topics of inte
 rest in harmonic analysis. In this talk we discuss a recent development of
  a novel\, multilinear singular integral theory that incorporates matrix w
 eights. First\, we develop from scratch a theory of multilinear Muckenhoup
 t classes for matrix weights\, using techniques inspired from convex combi
 natorics and differential geometry. Next\, we fully characterize the actio
 n of multilinear Calderón--Zygmund operators and (sub)multilinear maximal
  functions on cartesian products of matrix weighted Lebesgue spaces. On th
 e one hand\, we develop new versions of standard localization techniques s
 uch as sparse domination and Reverse Hölder inequalities. On the other ha
 nd\, we introduce a new concept of directional non-degeneracy for integral
  kernels. Thus\, we generalize and unify several previous results of the s
 calar and/or linear theories.\n\nThis talk is based on joint work with Dr.
  Zoe Nieraeth (Instituto de Matemáticas Universidad de Sevilla (IMUS)).\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/118/
URL:https://cesnet.zoom.us/j/99825599862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Predojević (University of Zagreb)
DTSTART:20260311T094000Z
DTEND:20260311T104000Z
DTSTAMP:20260315T015022Z
UID:FunctionSpaces/119
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/119/">Joint upper Banach density\, VC dimension\, and Euclidean point c
 onfigurations</a>\nby Bruno Predojević (University of Zagreb) as part of 
 Function spaces\n\n\nAbstract\nWe present two related results concerning t
 he existence of large copies\nof Euclidean point configurations in large s
 ets.\nThe first result generalises a classic conjecture of Szekély. More 
 precisely\,\nwe provide a sufficient condition on two measurable subsets o
 f the plane that\nensures all sufficiently large distances between them ar
 e realised.\nThe second result concerns the Vapnik–Chervonenkis dimensio
 n of a certain\ngeometric family of sets. Specifically\, for a sufficientl
 y regular curve $\\Gamma$ and for all\nsufficiently large scales $t>0$\, w
 e show that the family consisting of portions of\ntranslates of $t\\Gamma$
  attains the maximal possible Vapnik–Chervonenkis dimension.\nThese two 
 seemingly distinct problems are unified by a new notion that we\nintroduce
  in the talk: Joint upper Banach density.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/119/
END:VEVENT
END:VCALENDAR