BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Georgios Dosidis (University of Missouri\, Columbia) DTSTART;VALUE=DATE-TIME:20201008T134000Z DTEND;VALUE=DATE-TIME:20201008T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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:20240328T204332Z 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 BEGIN:VEVENT SUMMARY:Olli Tapiola (Universitat Autònoma de Barcelona) DTSTART;VALUE=DATE-TIME:20221013T134000Z DTEND;VALUE=DATE-TIME:20221013T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/66 DESCRIPTION:Title: John conditions\, Harnack chains and boundary Poincaré inequaliti es\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;VALUE=DATE-TIME:20221027T134000Z DTEND;VALUE=DATE-TIME:20221027T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/67 DESCRIPTION:Title: Regularity for nonlocal problems with non-standard growth\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;VALUE=DATE-TIME:20221110T144000Z DTEND;VALUE=DATE-TIME:20221110T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/68 DESCRIPTION:Title: Boundedness of Wolff-type potentials\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;VALUE=DATE-TIME:20221020T134000Z DTEND;VALUE=DATE-TIME:20221020T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/69 DESCRIPTION:Title: 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;VALUE=DATE-TIME:20221103T144000Z DTEND;VALUE=DATE-TIME:20221103T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/70 DESCRIPTION:Title: Dyadic multiparameter $\\mathrm{BMO}$ spaces\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;VALUE=DATE-TIME:20221124T144000Z DTEND;VALUE=DATE-TIME:20221124T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/71 DESCRIPTION:Title: Directional averages in codimension one\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;VALUE=DATE-TIME:20221215T144000Z DTEND;VALUE=DATE-TIME:20221215T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/72 DESCRIPTION:Title: Extrapolation in quasi-Banach function spaces\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;VALUE=DATE-TIME:20221222T144000Z DTEND;VALUE=DATE-TIME:20221222T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/73 DESCRIPTION:Title: Equivalences of (quasi-)norms in a certain vector-valued function space and its applications to multilinear operators\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;VALUE=DATE-TIME:20230504T134000Z DTEND;VALUE=DATE-TIME:20230504T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/74 DESCRIPTION:Title: Dimension-free $L^p$ estimates for the vector of maximal Riesz tra nsforms\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;VALUE=DATE-TIME:20230216T144000Z DTEND;VALUE=DATE-TIME:20230216T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/75 DESCRIPTION:Title: A different approach to endpoint weak-type estimates for Calderón -Zygmund operators\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;VALUE=DATE-TIME:20230316T144000Z DTEND;VALUE=DATE-TIME:20230316T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/76 DESCRIPTION:Title: $L^p$ improving continuity estimates and sparse bounds for the bil inear spherical maximal function\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;VALUE=DATE-TIME:20230223T144000Z DTEND;VALUE=DATE-TIME:20230223T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/77 DESCRIPTION:Title: Singular integrals along variable codimension one subspaces\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;VALUE=DATE-TIME:20230302T144000Z DTEND;VALUE=DATE-TIME:20230302T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/78 DESCRIPTION:Title: Nonlocal gradient potential estimates\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;VALUE=DATE-TIME:20230323T144000Z DTEND;VALUE=DATE-TIME:20230323T154000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/79 DESCRIPTION:Title: A Harmonic Analysis perspective on $W^{s\,p}$ as $s \\to 1^-$\ 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;VALUE=DATE-TIME:20230406T134000Z DTEND;VALUE=DATE-TIME:20230406T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/80 DESCRIPTION:Title: Construction of a phase space localizing operator\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;VALUE=DATE-TIME:20230413T134000Z DTEND;VALUE=DATE-TIME:20230413T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/81 DESCRIPTION:Title: About the decay of the Fourier transform of self-similar measures on the complex plane\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;VALUE=DATE-TIME:20230427T134000Z DTEND;VALUE=DATE-TIME:20230427T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/82 DESCRIPTION:Title: A variational theory for integral functionals involving finite-hor izon fractional gradients\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;VALUE=DATE-TIME:20230330T134000Z DTEND;VALUE=DATE-TIME:20230330T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/83 DESCRIPTION:Title: Fractional differentiability and (p\,q)-growth\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;VALUE=DATE-TIME:20230420T134000Z DTEND;VALUE=DATE-TIME:20230420T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/84 DESCRIPTION:Title: Modulation Invariant Operators near $L^1$\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;VALUE=DATE-TIME:20230518T134000Z DTEND;VALUE=DATE-TIME:20230518T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/85 DESCRIPTION:Title: Endpoint regularity bounds of maximal operators in higher dimensio ns\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;VALUE=DATE-TIME:20230511T134000Z DTEND;VALUE=DATE-TIME:20230511T144000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/86 DESCRIPTION:Title: 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;VALUE=DATE-TIME:20231024T120000Z DTEND;VALUE=DATE-TIME:20231024T130000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/87 DESCRIPTION:Title: Everywhere and partial regularity for parabolic systems with gener al growth\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}
Theory of Function Spaces: On Classical Tools for Modern Spaces\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;VALUE=DATE-TIME:20231205T130000Z
DTEND;VALUE=DATE-TIME:20231205T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T204332Z
UID:FunctionSpaces/89
DESCRIPTION:Title: Some remarks on the weak Harnack inequality for unbounded minimiz
ers of elliptic functionals with generalized Orlicz growth\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;VALUE=DATE-TIME:20231219T130000Z
DTEND;VALUE=DATE-TIME:20231219T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T204332Z
UID:FunctionSpaces/90
DESCRIPTION:Title: A discrete framework for the interpolation of Banach spaces\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;VALUE=DATE-TIME:20231121T130000Z
DTEND;VALUE=DATE-TIME:20231121T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T204332Z
UID:FunctionSpaces/91
DESCRIPTION:Title: Brascamp-Lieb Inequalities: Their Theory and Some Applications
\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;VALUE=DATE-TIME:20231107T130000Z
DTEND;VALUE=DATE-TIME:20231107T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T204332Z
UID:FunctionSpaces/92
DESCRIPTION:Title: BMO estimates for Hodge-Maxwell systems with discontinuous anisotr
opic coefficients\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;VALUE=DATE-TIME:20240220T130000Z
DTEND;VALUE=DATE-TIME:20240220T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T204332Z
UID:FunctionSpaces/93
DESCRIPTION:Title: Parabolic Muckenhoupt weights\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;VALUE=DATE-TIME:20240319T130000Z
DTEND;VALUE=DATE-TIME:20240319T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T204332Z
UID:FunctionSpaces/94
DESCRIPTION:Title: Around Hardy's inequality for convex sets\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;VALUE=DATE-TIME:20240402T120000Z
DTEND;VALUE=DATE-TIME:20240402T130000Z
DTSTAMP;VALUE=DATE-TIME:20240328T204332Z
UID:FunctionSpaces/95
DESCRIPTION:Title: On Morrey's inequality in fractional Sobolev spaces.\nby Firoj
Sk (University of Oldenburg) as part of Function spaces\n\nInteractive li
vestream: https://cesnet.zoom.us/j/99825599862\n\nAbstract\nWe study the s
harp constant in Morrey's inequality for fractional Sobolev spaces on the
entire Euclidean space of dimension N\, when 01 are such that s
p>N. In a series of recent articles by Hynd and Seuffert\, we discuss the
existence of the Morrrey extremals together with some regularity results.
We analyse the sharp asymptotic behaviour of the Morrey constant in the fo
llowing cases:\n\ni) when N\, p are fixed with N
A relaxation approach for the minimisation of the neo-Hookean ener gy\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;VALUE=DATE-TIME:20240416T120000Z DTEND;VALUE=DATE-TIME:20240416T130000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/97 DESCRIPTION:by Emil Airta (University of Málaga) as part of Function spac es\n\nInteractive livestream: https://cesnet.zoom.us/j/99825599862\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/FunctionSpaces/97/ URL:https://cesnet.zoom.us/j/99825599862 END:VEVENT BEGIN:VEVENT SUMMARY:Valentina Ciccone (University of Bonn) DTSTART;VALUE=DATE-TIME:20240430T120000Z DTEND;VALUE=DATE-TIME:20240430T130000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/98 DESCRIPTION:by Valentina Ciccone (University of Bonn) as part of Function spaces\n\nInteractive livestream: https://cesnet.zoom.us/j/99825599862\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/FunctionSpaces/98/ URL:https://cesnet.zoom.us/j/99825599862 END:VEVENT BEGIN:VEVENT SUMMARY:Arran Fernandez (Eastern Mediterranean University) DTSTART;VALUE=DATE-TIME:20240423T120000Z DTEND;VALUE=DATE-TIME:20240423T130000Z DTSTAMP;VALUE=DATE-TIME:20240328T204332Z UID:FunctionSpaces/99 DESCRIPTION:Title: Function spaces for fractional integrals and derivatives\nby A rran Fernandez (Eastern Mediterranean University) as part of Function spac es\n\nInteractive livestream: https://cesnet.zoom.us/j/99825599862\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/FunctionSpaces/99/ URL:https://cesnet.zoom.us/j/99825599862 END:VEVENT END:VCALENDAR