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BEGIN:VEVENT
SUMMARY:Georgios Dosidis (University of Missouri\, Columbia)
DTSTART;VALUE=DATE-TIME:20201008T134000Z
DTEND;VALUE=DATE-TIME:20201008T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/1
DESCRIPTION:Title: Linear and multilinear spherical maximal functions\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;VALUE=DATE-TIME:20201022T134000Z
DTEND;VALUE=DATE-TIME:20201022T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/2
DESCRIPTION:Title: Optimal Sobolev embeddings for symmetric gradients (joint work with
Andrea Cianchi)\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;VALUE=DATE-TIME:20201015T134000Z
DTEND;VALUE=DATE-TIME:20201015T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/3
DESCRIPTION:Title: Norm inequalities for linear and multilinear singular integrals on
weighted and variable exponent Hardy spaces\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;VALUE=DATE-TIME:20201029T144000Z
DTEND;VALUE=DATE-TIME:20201029T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/4
DESCRIPTION:Title: Factorization of function spaces and pointwise multipliers\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;VALUE=DATE-TIME:20201105T144000Z
DTEND;VALUE=DATE-TIME:20201105T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/5
DESCRIPTION:Title: On Limiting Approximation Spaces with Slowly Varying Functions\
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;VALUE=DATE-TIME:20201112T144000Z
DTEND;VALUE=DATE-TIME:20201112T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/6
DESCRIPTION:Title: A Normal Form for Hardy Inequalities\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 *normal form Hardy
inequality*.\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;VALUE=DATE-TIME:20210107T140000Z
DTEND;VALUE=DATE-TIME:20210107T150000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/7
DESCRIPTION:Title: Optimal embeddings for fractional-order Orlicz-Sobolev spaces\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;VALUE=DATE-TIME:20201119T144000Z
DTEND;VALUE=DATE-TIME:20201119T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/8
DESCRIPTION:Title: Elliptic Equations with Degenerate Weights\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;VALUE=DATE-TIME:20201126T144000Z
DTEND;VALUE=DATE-TIME:20201126T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/9
DESCRIPTION:Title: Extremal functions for Sobolev Embedding and non-linear problems\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;VALUE=DATE-TIME:20201203T144000Z
DTEND;VALUE=DATE-TIME:20201203T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/10
DESCRIPTION:Title: Strongly nonlinear multiplicative inequalities\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;VALUE=DATE-TIME:20201217T144000Z
DTEND;VALUE=DATE-TIME:20201217T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/11
DESCRIPTION:Title: An extended variational approach for nonlinear PDE via modular spa
ces\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;VALUE=DATE-TIME:20210114T144000Z
DTEND;VALUE=DATE-TIME:20210114T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/12
DESCRIPTION:Title: Limits of fractional Orlicz-Sobolev spaces\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;VALUE=DATE-TIME:20210121T144000Z
DTEND;VALUE=DATE-TIME:20210121T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/13
DESCRIPTION:Title: Vector-valued Sobolev spaces based on Banach function spaces\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;VALUE=DATE-TIME:20210128T144000Z
DTEND;VALUE=DATE-TIME:20210128T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/14
DESCRIPTION:Title: 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;VALUE=DATE-TIME:20201210T144000Z
DTEND;VALUE=DATE-TIME:20201210T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/15
DESCRIPTION:Title: Co-area formula for maps into metric spaces\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;VALUE=DATE-TIME:20210204T144000Z
DTEND;VALUE=DATE-TIME:20210204T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/16
DESCRIPTION:Title: Fractional Poincaré inequalities and Harmonic Analysis\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;VALUE=DATE-TIME:20210218T144000Z
DTEND;VALUE=DATE-TIME:20210218T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/17
DESCRIPTION:Title: Boundedness of Bochner-Riesz operators on rearrangement invariant
spaces\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;VALUE=DATE-TIME:20210225T144000Z
DTEND;VALUE=DATE-TIME:20210225T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/18
DESCRIPTION:Title: Optimal doubling measures and applications to graphs\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;VALUE=DATE-TIME:20210304T144000Z
DTEND;VALUE=DATE-TIME:20210304T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/19
DESCRIPTION:Title: Regularity and uniqueness results in some variational problems
\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;VALUE=DATE-TIME:20210211T144000Z
DTEND;VALUE=DATE-TIME:20210211T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/20
DESCRIPTION:Title: Continuity properties of analytic pseudodifferential operators
\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;VALUE=DATE-TIME:20210311T144000Z
DTEND;VALUE=DATE-TIME:20210311T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/21
DESCRIPTION:Title: Variable exponent Bochner–Lebesgue spaces with symmetric gradien
t structure\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;VALUE=DATE-TIME:20210415T134000Z
DTEND;VALUE=DATE-TIME:20210415T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/22
DESCRIPTION:Title: Interpolation of compact bilinear operators\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;VALUE=DATE-TIME:20210318T144000Z
DTEND;VALUE=DATE-TIME:20210318T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/23
DESCRIPTION:Title: Completeness of sets of shifts in invariant Banach spaces of funct
ions\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;VALUE=DATE-TIME:20210325T144000Z
DTEND;VALUE=DATE-TIME:20210325T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/24
DESCRIPTION:Title: Consequences of the Kadison Singer solution and Weaver's conjectur
e for the recovery of multivariate functions from a few random samples
\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;VALUE=DATE-TIME:20210408T134000Z
DTEND;VALUE=DATE-TIME:20210408T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/26
DESCRIPTION:Title: The decreasing rearrangement and mean oscillation\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;VALUE=DATE-TIME:20210422T134000Z
DTEND;VALUE=DATE-TIME:20210422T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/27
DESCRIPTION:Title: Dirichlet problem for functions of least gradient in domains with
boundary of positive mean curvature in metric measure spaces\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;VALUE=DATE-TIME:20210401T134000Z
DTEND;VALUE=DATE-TIME:20210401T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/28
DESCRIPTION:Title: General Reiteration Theorems for $\\mathcal{R}$ and $\\mathcal{L}$
spaces\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;VALUE=DATE-TIME:20210429T134000Z
DTEND;VALUE=DATE-TIME:20210429T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/29
DESCRIPTION:Title: Stationary Navier-Stokes flow with irregular Dirichlet data\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;VALUE=DATE-TIME:20210513T134000Z
DTEND;VALUE=DATE-TIME:20210513T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/30
DESCRIPTION:Title: Uniformization of weighted Gromov hyperbolic spaces and uniformly
locally bounded geometry\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;VALUE=DATE-TIME:20210520T134000Z
DTEND;VALUE=DATE-TIME:20210520T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/31
DESCRIPTION:Title: Estimates of Besov mixed-type norms for functions in Sobolev and H
ardy-Sobolev spaces\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;VALUE=DATE-TIME:20210603T134000Z
DTEND;VALUE=DATE-TIME:20210603T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/32
DESCRIPTION:Title: Sobolev maps to the circle\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;VALUE=DATE-TIME:20210527T134000Z
DTEND;VALUE=DATE-TIME:20210527T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/33
DESCRIPTION:Title: Distilling Rubio de Francia's extrapolation theorem\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;VALUE=DATE-TIME:20210617T134000Z
DTEND;VALUE=DATE-TIME:20210617T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/34
DESCRIPTION:Title: Singular Brascamp-Lieb inequalities with cubical structure\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;VALUE=DATE-TIME:20210701T134000Z
DTEND;VALUE=DATE-TIME:20210701T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/35
DESCRIPTION:Title: Estimates for the Hopf invariant in critical fractional Sobolev sp
aces\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;VALUE=DATE-TIME:20210624T134000Z
DTEND;VALUE=DATE-TIME:20210624T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/36
DESCRIPTION:Title: On the John-Nirenberg space\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;VALUE=DATE-TIME:20210506T134000Z
DTEND;VALUE=DATE-TIME:20210506T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/37
DESCRIPTION:Title: The infinite Hilbert matrix on spaces of analytic functions\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;VALUE=DATE-TIME:20210610T134000Z
DTEND;VALUE=DATE-TIME:20210610T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/38
DESCRIPTION:Title: The spaces $BMO_{(s)}$ and o-O structures\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;VALUE=DATE-TIME:20220203T144000Z
DTEND;VALUE=DATE-TIME:20220203T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/39
DESCRIPTION:Title: From Fourier series to multilinear analysis\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;VALUE=DATE-TIME:20220210T144000Z
DTEND;VALUE=DATE-TIME:20220210T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/40
DESCRIPTION:Title: Decreasing rearrangements on average operators\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;VALUE=DATE-TIME:20220217T144000Z
DTEND;VALUE=DATE-TIME:20220217T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/41
DESCRIPTION:Title: An Atomic Decomposition for Divergence Free Measures\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;VALUE=DATE-TIME:20220224T144000Z
DTEND;VALUE=DATE-TIME:20220224T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/42
DESCRIPTION:Title: Perturbations beyond Schauder\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;VALUE=DATE-TIME:20220324T144000Z
DTEND;VALUE=DATE-TIME:20220324T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/43
DESCRIPTION:Title: (Generalized) Sobolev-Orlicz Spaces of differential forms\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;VALUE=DATE-TIME:20211104T144000Z
DTEND;VALUE=DATE-TIME:20211104T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/44
DESCRIPTION:Title: On the interpolation constants for variable Lebesgue spaces\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;VALUE=DATE-TIME:20211111T144000Z
DTEND;VALUE=DATE-TIME:20211111T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/45
DESCRIPTION:Title: Stability for geometric and functional inequalities\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;VALUE=DATE-TIME:20211118T144000Z
DTEND;VALUE=DATE-TIME:20211118T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/46
DESCRIPTION:Title: Approximation properties of Musielak-Orlicz-Sobolev spaces and its
role in well-posedness of nonstandard growth PDE\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;VALUE=DATE-TIME:20211209T144000Z
DTEND;VALUE=DATE-TIME:20211209T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/47
DESCRIPTION:Title: Outer $L^p$ spaces: Köthe duality\, Minkowski inequality and more
\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;VALUE=DATE-TIME:20211216T144000Z
DTEND;VALUE=DATE-TIME:20211216T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/48
DESCRIPTION:Title: Closures of planar BV homeomorphisms and the relaxation of functio
nals with linear growth\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;VALUE=DATE-TIME:20220106T144000Z
DTEND;VALUE=DATE-TIME:20220106T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/49
DESCRIPTION:Title: A-quasiconvexity\, function spaces and regularity\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;VALUE=DATE-TIME:20220113T144000Z
DTEND;VALUE=DATE-TIME:20220113T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/50
DESCRIPTION:Title: New results for non-autonomous functionals with mild phase transit
ion\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;VALUE=DATE-TIME:20220120T144000Z
DTEND;VALUE=DATE-TIME:20220120T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/51
DESCRIPTION:Title: On the Embedding of BV Space into Besov-Orlicz Space\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;VALUE=DATE-TIME:20220127T144000Z
DTEND;VALUE=DATE-TIME:20220127T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/52
DESCRIPTION:Title: Symmetrization for fractional elliptic problems: a direct approach
\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;VALUE=DATE-TIME:20220310T144000Z
DTEND;VALUE=DATE-TIME:20220310T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/53
DESCRIPTION:Title: One-sided sparse domination\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;VALUE=DATE-TIME:20220317T144000Z
DTEND;VALUE=DATE-TIME:20220317T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/54
DESCRIPTION:Title: Nonlinear spaces of functions and compensated compactness for conc
entrations\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 arXiv:2106.03077.\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;VALUE=DATE-TIME:20220303T144000Z
DTEND;VALUE=DATE-TIME:20220303T154000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/55
DESCRIPTION:Title: Functionals with nonstandard growth and convex duality\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;VALUE=DATE-TIME:20220331T134000Z
DTEND;VALUE=DATE-TIME:20220331T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/56
DESCRIPTION:Title: Construction of a right inverse for the divergence in non-cylindri
cal time dependent domains\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;VALUE=DATE-TIME:20220414T134000Z
DTEND;VALUE=DATE-TIME:20220414T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/57
DESCRIPTION:Title: Anisotropic generalized Orlicz spaces and PDE\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;VALUE=DATE-TIME:20220505T134000Z
DTEND;VALUE=DATE-TIME:20220505T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/58
DESCRIPTION:Title: Nikodym-type spherical maximal functions\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;VALUE=DATE-TIME:20220421T134000Z
DTEND;VALUE=DATE-TIME:20220421T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/60
DESCRIPTION:Title: Subelliptic pseudo-differential calculus on compact Lie groups
\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;VALUE=DATE-TIME:20220407T134000Z
DTEND;VALUE=DATE-TIME:20220407T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/61
DESCRIPTION:Title: Sobolev spaces and spectral asymptotics for commutators\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;VALUE=DATE-TIME:20220428T134000Z
DTEND;VALUE=DATE-TIME:20220428T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/62
DESCRIPTION:Title: New estimates for the maximal functions and applications\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;VALUE=DATE-TIME:20220519T134000Z
DTEND;VALUE=DATE-TIME:20220519T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/63
DESCRIPTION:Title: Sparse approximation for break of scale embeddings\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;VALUE=DATE-TIME:20220512T134000Z
DTEND;VALUE=DATE-TIME:20220512T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/64
DESCRIPTION:Title: On Rigidity\, Flexibility and Scaling Laws: The Tartar Square\
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;VALUE=DATE-TIME:20220526T134000Z
DTEND;VALUE=DATE-TIME:20220526T144000Z
DTSTAMP;VALUE=DATE-TIME:20220816T033519Z
UID:FunctionSpaces/65
DESCRIPTION:Title: Dunkl translations\, Dunkl--type $BMO$ space and Riesz transforms
for Dunkl transform on $L^\\infty$\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
END:VCALENDAR