BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Nicola Arcozzi (University of Bologna)
DTSTART;VALUE=DATE-TIME:20200916T160000Z
DTEND;VALUE=DATE-TIME:20200916T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/1
DESCRIPTION:Title: The
Hardy space from an engineer's perspective\nby Nicola Arcozzi (Univer
sity of Bologna) as part of Harmonic analysis e-seminars\n\n\nAbstract\nTh
e Hardy space $H^2$ made its way into signal theory since Wiener's time\,
and it belongs to the standard toolbox of all engineers who deal with sign
als. We will see how $H^2$ and its related function spaces $H^1$\, $H^\\in
fty$\, and $BMOA$ arise from basic practical problems\, and how multiplica
tion\, Toeplitz\, and Hankel operators enter the picture. Feedback systems
will take us at the front step of Pick interpolation. The aim is advertis
ing a possible intuition of a beautiful chapter of pure mathematics.\n
LOCATION:https://researchseminars.org/talk/HAeS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Negro (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20201021T160000Z
DTEND;VALUE=DATE-TIME:20201021T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/2
DESCRIPTION:Title: Sha
rp estimates for the wave equation via the Penrose transform\nby Giuse
ppe Negro (University of Birmingham) as part of Harmonic analysis e-semina
rs\n\n\nAbstract\nIn 2004\, Foschi found the best constant\, and the extre
mizing functions\, for the Strichartz inequality for the wave equation wi
th data in the Sobolev space $\\Hdot^{1/2}\\times\\Hdot^{-1/2}(\\R^3)$. H
e also formulated a conjecture\, concerning the extremizers to this Stric
hartz inequality in all spatial dimensions $d\\ge 2$. We disprove such co
njecture for even $d$\, but we provide evidence to support it for odd $d$.
The proofs use the conformal compactification of the Minkowski space-tim
e given by the Penrose transform.\n
LOCATION:https://researchseminars.org/talk/HAeS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Duoandikoetxea (Euskal Herriko Unibertsitatea)
DTSTART;VALUE=DATE-TIME:20200930T160000Z
DTEND;VALUE=DATE-TIME:20200930T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/3
DESCRIPTION:Title: Wei
ghted Morrey spaces\nby Javier Duoandikoetxea (Euskal Herriko Uniberts
itatea) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThis talk i
s an account of my work on Morrey spaces with Marcel \nRosenthal in recent
years.\n\nThere are several definitions for weighted Morrey spaces. We ob
tain \nboundedness results in all of them for operators satisfying the \na
ssumptions of the usual extrapolation theorem\, that is\, we get \nweighte
d Morrey estimates from weighted Lebesgue estimates with $A_p$ \nweights.
The results can be applied to a variety of operators and \ntogether with
the norm estimates\, our technique also provides the \ndefinition of the o
perator by embedding.\n\nRecently we obtained results for a more general c
lass of weighted \nMorrey spaces from an extension of the usual Muckenhoup
t condition to \nthe Morrey setting\, involving the Khöthe dual of the sp
ace. In some \ncases the conditions characterize the weighted inequalities
of maximal \noperators.\n
LOCATION:https://researchseminars.org/talk/HAeS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ujué Etayo (TUGraz)
DTSTART;VALUE=DATE-TIME:20201111T170000Z
DTEND;VALUE=DATE-TIME:20201111T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/4
DESCRIPTION:Title: A B
ombieri-type inequality for Weierstrass sigma functions\nby Ujué Etay
o (TUGraz) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe Bomb
ieri inequality is a classic inequality in number theory\,see [B. Beauzamy
\, E. Bombieri\, P. Enflo\, and H. L. Montgomery. Products\nof polynomials
in many variables. Journal of Number Theory\, 36(2):219\n– 245\, 1990)]
.\nThe original statement says that given two homogeneous polynomials on $
N$ variables $P\,Q$ respectively of degree $m$ and $n$\, then\n$$\n{\\frac
{m!n!}{(m+n)!}}\\|P\\|^{2}\\\,\\|Q\\|^{2}\\leq \\|P\\cdot Q\\|^{2}\\leq \
\|P\\|^{2}\\\,\\|Q\\|^{2}\,\n$$\nwhere the norm is the Bombieri-Weyl norm.
\nThis inequality admits a rewriting in terms of integrals on the sphere\,
a property exploited in [U. Etayo. A sharp bombieri inequality\, logarith
mic energy and well con-\nditioned polynomials\, 2019].\nIn a joint work w
ith Joaquim Ortega-Cerd\\`a and Haakan Hedenmalm\, we use this new definit
ion to generalize the inequality to other Riemannian manifolds\, in partic
ular the torus $\\mathbb{C}/\\Lambda$\n
LOCATION:https://researchseminars.org/talk/HAeS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Decio (Norwegian University of Science and Technology)
DTSTART;VALUE=DATE-TIME:20201028T170000Z
DTEND;VALUE=DATE-TIME:20201028T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/5
DESCRIPTION:Title: Nod
al sets of Steklov eigenfunctions\nby Stefano Decio (Norwegian Univers
ity of Science and Technology) as part of Harmonic analysis e-seminars\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/HAeS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Bruno (Ghent University)
DTSTART;VALUE=DATE-TIME:20201014T160000Z
DTEND;VALUE=DATE-TIME:20201014T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/6
DESCRIPTION:Title: Fac
torization properties of smooth functions and vectors\nby Tommaso Brun
o (Ghent University) as part of Harmonic analysis e-seminars\n\n\nAbstract
\nGiven a module $\\mathcal{M}$ over a non-unital algebra $\\mathcal{A}$\,
we say that $\\mathcal{M}$ has the weak factorization property if $\\math
cal{M}= \\mathrm{span} \\{\\mathcal{A} \\cdot \\mathcal{M}\\}$\, while it
has the strong factorization property if $\\mathcal{M}= \\mathcal{A} \\cdo
t \\mathcal{M}$. In this talk we shall review old and recent results about
strong and weak factorizations of smooth functions and smooth vectors of
Lie group representations. We shall also discuss open problems and current
lines of research.\n
LOCATION:https://researchseminars.org/talk/HAeS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Luis Romero (University of Vienna)
DTSTART;VALUE=DATE-TIME:20201202T174000Z
DTEND;VALUE=DATE-TIME:20201202T184000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/7
DESCRIPTION:Title: Sam
pling\, density\, and equidistribution\nby José Luis Romero (Universi
ty of Vienna) as part of Harmonic analysis e-seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/HAeS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gennady Uraltsev (Cornell University)
DTSTART;VALUE=DATE-TIME:20201209T170000Z
DTEND;VALUE=DATE-TIME:20201209T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/8
DESCRIPTION:Title: Som
e results in Banach space-valued time frequency analysis\nby Gennady U
raltsev (Cornell University) as part of Harmonic analysis e-seminars\n\n\n
Abstract\nSIO (Singular Integral Operator) theory and\, Calderón-Zygmund
theory specifically\, developed starting from the '60s\, provides a vast a
rray of tools for dealing with operators that resemble the Hilbert transfo
rm\n$$\n\\mathrm{H}f(x):= \\int_{\\mathbb R}f(x-y)\\frac{d y}{y}\,\n$$\n\n
an ubiquitous operator in Complex Analysis\, semi-linear PDEs\, and many o
ther branches of mathematics. Results valid for -valued functions were ext
ended to Banach spaces-valued functions thanks to Bourgain's groundbreakin
g work on the deep relation between Banach space geometry and boundedness
properties of vector-valued SIOs.\n\nScalar-valued bounds for multilinear
SIOs\, like the bilinear Hilbert transform\n\n$$\n\\mathrm{BHT}[f_{1}\,f_{
2}](x)=\\int_{\\mathbb R} f_{1}(x-t) f_{2}(x+t) \\frac{d t} {t}\,\n$$\n \n
are classic in time-frequency-scale analysis. Banach-space valued results
have appeared only in the last couple of years. The well understood connec
tions with Banach space geometry from linear theory are just starting to b
e investigated.\n\nOpen questions and generalizations to non-commutative a
nalysis abound and would come hand-in-hand with progress in understanding
SIOs with worse singularities than of Calderón-Zygmund type that can ofte
n be realized as SIO-valued CZ operators.\n
LOCATION:https://researchseminars.org/talk/HAeS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Martini (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20210113T170000Z
DTEND;VALUE=DATE-TIME:20210113T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/9
DESCRIPTION:Title: Spe
ctral multipliers for sub-Laplacians: recent developments and open problem
s\nby Alessio Martini (University of Birmingham) as part of Harmonic a
nalysis e-seminars\n\n\nAbstract\nI will present some old and new results
about the $L^p$ functional calculus for sub-Laplacians $L$. It has been kn
own for a long time that\, under quite general assumptions on the sub-Lapl
acian and the underlying sub-Riemannian structure\, an operator of the for
m $F(L)$ is bounded on $L^p$\, $1< p<\\infty$\, whenever the multiplier $
F$ satisfies a scale-invariant smoothness condition of sufficiently larger
order.\nThe problem of determining the minimal smoothness assumptions\, h
owever\, remains widely open and will be the focus of our discussion.\n
LOCATION:https://researchseminars.org/talk/HAeS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giona Veronelli (Università di Milano-Bicocca)
DTSTART;VALUE=DATE-TIME:20210210T170000Z
DTEND;VALUE=DATE-TIME:20210210T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/10
DESCRIPTION:Title: So
bolev spaces on manifolds with lower bounded curvature\nby Giona Veron
elli (Università di Milano-Bicocca) as part of Harmonic analysis e-semina
rs\n\n\nAbstract\nThere are several notions of Sobolev spaces on a Riemann
ian manifold: from the operator theory viewpoint it is natural to consider
Sobolev functions defined by taking the $L^p$ norms of functions and of p
owers of their Laplacian. Instead\, the regularity theory of elliptic equa
tions involves Sobolev functions defined via the $L^p$ norm of all the de
rivatives up to a certain order. Moreover\, Sobolev spaces can be characte
rized via compactly supported smooth approximations.\nIn this talk\, we wi
ll focus on non-compact manifolds with lower bounded curvature. We will di
scuss some results giving the (non)-equivalence between the different Sobo
lev spaces. In particular\, we will highlight the role played in the theor
y by the Calderon-Zygmund inequality and the Bochner formulas\, and we wil
l sketch how to exploit singular metric spaces (e.g. Alexandrov or RCD) as
a tool to construct smooth counterexamples.\n
LOCATION:https://researchseminars.org/talk/HAeS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Vallarino (Politecnico di Torino)
DTSTART;VALUE=DATE-TIME:20210317T170000Z
DTEND;VALUE=DATE-TIME:20210317T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/11
DESCRIPTION:Title: An
alysis on trees with nondoubling flows\nby Maria Vallarino (Politecnic
o di Torino) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe cl
assical Calderón–Zygmund theory was developed in the Euclidean space an
d\,\nmore generally\, on spaces of homogeneous type\, which are measure me
tric spaces with\nthe doubling property.\nIn this talk we consider trees e
ndowed with flow measures\, which are nondoubling measures of at least exp
onential growth. In this setting\, we develop a Calderón–Zygmund\ntheor
y and we define $BMO$ and Hardy spaces\, proving a number of desired resul
ts extending the corresponding theory as known in the classical setting.\n
This is a joint work with Matteo Levi\, Federico Santagati and Anita Tabac
co.\n
LOCATION:https://researchseminars.org/talk/HAeS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fulvio Ricci (Scuola Normale Superiore)
DTSTART;VALUE=DATE-TIME:20210224T170000Z
DTEND;VALUE=DATE-TIME:20210224T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/12
DESCRIPTION:Title: Mu
lti-parameter structures\nby Fulvio Ricci (Scuola Normale Superiore) a
s part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk we give
a survey on a certain number of multi-parameter structures\, on $\\mathbb
R^n$ and on nilpotent groups\, that have been introduced in the last 20 y
ears. They include flag and multi-norm structures.\nThese structures are i
ntermediate between the one-parameter dilation structures of standard Cald
erón-Zygmund theory and the full $n$-parameter product structure. Each st
ructure has its own type of maximal functions\, singular integral operator
s\, square functions\, Hardy spaces.\n
LOCATION:https://researchseminars.org/talk/HAeS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loredana Lanzani (Syracuse University)
DTSTART;VALUE=DATE-TIME:20210331T160000Z
DTEND;VALUE=DATE-TIME:20210331T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/13
DESCRIPTION:Title: Th
e commutator of the Cauchy-Szegő projection for domains in $C^n$ with min
imal smoothness\nby Loredana Lanzani (Syracuse University) as part of
Harmonic analysis e-seminars\n\n\nAbstract\nLet $D\\subset\\C^n$ be a boun
ded\, strongly pseudoconvex domain whose boundary $bD$ satisfies the minim
al regularity condition of class $C^2$.\nWe characterize boundedness and c
ompactness in $L^p(bD\, \\omega)$\,\, for $1< p < \\infty$\,of the commuta
tor $[b\,S_\\omega]$ where $S_\\omega$ is the Cauchy--Szegő (orthogonal)
projection of $L^2(bD\, \\omega)$ onto the holomorphic Hardy space $H^2(
bD\, \\omega)$\n and the measure $\\omega$ belongs to a family (the ``
Leray Levi-like'' measures)\n that includes induced Lebesgue measure $\\si
gma$. We next consider a much larger family of measures $\\{\\Omega_p\\}$
modeled after the Muckenhoupt $A_p$-weights for $\\sigma$:\n we define th
e holomorphic Hardy spaces $H^p(bD\, \\Omega_p)$ and we characterize\n bou
ndedness and compactness of $[b\, S_{\\Omega_2}]$ in $L^2(bD\, \\Omega_2)$
.\n Earlier closely related results rely upon an asymptotic expansion\, an
d subsequent pointwise estimates\, of the Cauchy--Szegő kernel that are n
ot available in the settings of minimal regularity {of $bD$} and/or $A_p$-
like measures. \n\n\n \n This is joint work with Xuan Thinh Duong\, Ji L
i and Brett D. Wick.\n
LOCATION:https://researchseminars.org/talk/HAeS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gian Maria Dall'Ara (Indam/Scuola Normale Superiore)
DTSTART;VALUE=DATE-TIME:20210324T170000Z
DTEND;VALUE=DATE-TIME:20210324T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/14
DESCRIPTION:Title: L^
p mapping problems for Bergman projections\nby Gian Maria Dall'Ara (In
dam/Scuola Normale Superiore) as part of Harmonic analysis e-seminars\n\n\
nAbstract\nThis is for the most part a survey talk. I will discuss various
as-\npects of the following problem: for which values of $p$ is the Bergm
an projection\nof a given domain in $\\mathbb C^n$ bounded on $L^p$? The a
nswer depends heavily on the\ncomplex geometry of the domain. We will disc
uss the problem in one and\nseveral variables\, its connection with the th
eory of conformal mappings and\nthat of singular integrals\, highlighting
many open problems.\n
LOCATION:https://researchseminars.org/talk/HAeS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan S. Trapasso (Università di Genova)
DTSTART;VALUE=DATE-TIME:20210421T160000Z
DTEND;VALUE=DATE-TIME:20210421T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/15
DESCRIPTION:Title: Di
spersion\, spreading and sparsity of Gabor wave packets\nby Ivan S. Tr
apasso (Università di Genova) as part of Harmonic analysis e-seminars\n\n
\nAbstract\nSparsity properties for phase-space representations of several
types of operators (including pseudodifferential\, metaplectic and Fourie
r integral operators) have been extensively studied in recent articles\, w
ith applications to the analysis of dispersive evolution equation. It has
been proved that such operators are approximately diagonalized by Gabor wa
ve packets - equivalently\, the corresponding phase-space representations
(Gabor matrix/kernel) can be thought of as sparse infinite-dimensional mat
rices. While wave packets are expected to undergo some spreading and dispe
rsion phenomena\, there is no record of these issues in the aforementioned
estimates. We recently proved refined estimates for the Gabor matrix of m
etaplectic operators\, also of generalized type\, where sparsity\, spreadi
ng and dispersive properties are all simultaneously noticeable. We also pr
ovide applications to the propagation of singularities for the Schr\\"odin
ger equation\; in this connection\, our results can be regarded as a micro
local refinement of known estimates. The talk is based on joint work with
Elena Cordero and Fabio Nicola.\n
LOCATION:https://researchseminars.org/talk/HAeS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fraccaroli (Universität Bonn)
DTSTART;VALUE=DATE-TIME:20210519T160000Z
DTEND;VALUE=DATE-TIME:20210519T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/16
DESCRIPTION:Title: Du
ality for outer $L^p$ spaces\nby Marco Fraccaroli (Universität Bonn)
as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe theory of $L^p$
spaces for outer measures\, or outer $L^p$ spaces\, was\ndeveloped by Do
and Thiele to encode the proof of boundedness of certain\nmultilinear oper
ators in a streamlined argument. Accordingly to this\npurpose\, the theory
was developed in the direction of the real\ninterpolation features of the
se spaces\, while other questions remained\nuntouched.\nFor example\, the
outer $L^p$ spaces are defined by quasi-norms\ngeneralizing the classical
mixed $L^p$ norms on sets with a Cartesian\nproduct structure. Therefore\,
it is natural to ask whether in arbitrary\nsettings the outer $L^p$ quasi
-norms are equivalent to norms. In this\ntalk\, we will answer this questi
on\, with a particular focus on certain\nsettings on the upper half space
$\\R^d \\times (0\,\\infty)$ related to the\nwork of Do and Thiele.\n
LOCATION:https://researchseminars.org/talk/HAeS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Brocchi
DTSTART;VALUE=DATE-TIME:20210616T163000Z
DTEND;VALUE=DATE-TIME:20210616T173000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/17
DESCRIPTION:Title: Sp
arse T1 theorems\nby Gianmarco Brocchi as part of Harmonic analysis e-
seminars\n\n\nAbstract\nMany operators in analysis are non-local\, in the
sense that a\n perturbation of the input near a point modifies the output
\n everywhere\; consider for example the operator that maps the initial\n
data to the corresponding solution of the heat equation.\n\n Sparse Dom
ination consists in controlling such operators by a sum of\n positive\, l
ocal averages. This allows to derive plenty of estimates\,\n which are of
ten optimal. For example\, it has been shown that Calderón--Zygmund opera
tors\n and square functions admit such a domination even under minimal $T
1$ hypotheses.\\newline\n\n In this talk we introduce the concept of spar
se domination\n and present a sparse $T1$ theorem for square functions\,\
n discussing the new difficulties and ideas in this case.\n\n Time perm
itting\, we will see how sparse domination can be applied\n in very diffe
rent context.\n
LOCATION:https://researchseminars.org/talk/HAeS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filippo De Mari (Università di Genova)
DTSTART;VALUE=DATE-TIME:20210630T160000Z
DTEND;VALUE=DATE-TIME:20210630T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/18
DESCRIPTION:Title: Vi
ews on the Radon Transform\nby Filippo De Mari (Università di Genova)
as part of Harmonic analysis e-seminars\n\n\nAbstract\nI will recall and
introduce some of the many existing Radon transforms\, focusing in particu
lar on the setup of $G$-dual pairs $(X\,\\Xi)$ introduced by Helgason more
than fifty years ago\, where $G$ is a locally compact group that acts tr
ansitively both on $X$ and $\\Xi$. \nI will then present some results obta
ined in collaboration with G. S. Alberti\, F. Bartolucci\, E. De Vito\, M
. Monti and F. Odone which bring into play (square integrable) representat
ions. If the functions to be analyzed live on $X$ and the quasi regular r
epresentation of $G$ on $L^2(X)$ and $L^2(\\Xi)$ are square integrable\, t
hen it is possible to write a nice inversion formula for the Radon transfo
rm associated to the families of submanifolds of $X$ that are prescribed b
y the object $\\Xi$ which is dual to $X$. This formula hinges on a unitari
zation of the Radon transform that may be proved in a rather general setup
if the quasi regular representations of $G$ on $L^2(X)$ and $L^2(\\Xi)$
are irreducible\, and on an intertwining property of the Radon transform.
The former result is inspired by work of Helgason. Some examples are disc
ussed\, mostly the guiding case related to shearlets that points in the di
rection of possible practical inversion techniques.\n
LOCATION:https://researchseminars.org/talk/HAeS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART;VALUE=DATE-TIME:20211006T160000Z
DTEND;VALUE=DATE-TIME:20211006T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/19
DESCRIPTION:Title: Fi
nite point configurations and the Vapnik-Chervonenkis dimension\nby Al
ex Iosevich (University of Rochester) as part of Harmonic analysis e-semin
ars\n\n\nAbstract\nThe Vapnik-Chervonenkis (VC) dimension was invented in
1970 to study learning models. This notion has since become one of the cor
nerstones of modern data science. This beautiful idea has also found appli
cations in other areas of mathematics. In this talk we are going to descri
be how the study of the VC-dimension in the context of families of indicat
or functions of spheres centered at points in sets of a given Hausdorff di
mension (or in sets of a given size inside vector spaces over finite field
s) gives rise to interesting\, and in some sense extremal\, point configur
ations.\n
LOCATION:https://researchseminars.org/talk/HAeS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karlheinz Gröchenig (University of Vienna)
DTSTART;VALUE=DATE-TIME:20211020T160000Z
DTEND;VALUE=DATE-TIME:20211020T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/20
DESCRIPTION:Title: Va
riable bandwidth and sampling theorems\nby Karlheinz Gröchenig (Univ
ersity of Vienna) as part of Harmonic analysis e-seminars\n\n\nAbstract\nW
e study sampling theorems in spectral subspaces of a uniformly elliptic di
fferential operator. For constant coefficients\, these are spaces of bandl
imited functions\, whereas for general elliptic operators\, the resulting
spaces consist of functions of "variable bandwidth". This is one of severa
l constructions that gives meaning to the intuitive notion of a local and
time-varying bandwidth. The interpretation is supported by the results on
sampling theorems and necessary sampling density.\n
LOCATION:https://researchseminars.org/talk/HAeS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART;VALUE=DATE-TIME:20211110T170000Z
DTEND;VALUE=DATE-TIME:20211110T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/21
DESCRIPTION:Title: Th
e Smoothest Average and New Uncertainty Principles for the Fourier Transfo
rm\nby Stefan Steinerberger (University of Washington) as part of Harm
onic analysis e-seminars\n\n\nAbstract\nSuppose you are given a real-value
d function f(x) and want to compute a local average at a certain scale. Wh
at we usually do is to pick a nice probability measure u\, centered at 0 a
nd having standard deviation at the desired scale\, and convolve. Classica
l candidates for u are the characteristic function or the Gaussian. This g
ot me interested in finding the ”best” function u – this problem com
es in two parts: (1) describing what one considers to be desirable propert
ies of the convolution and (2) understanding which functions satisfy these
properties. I tried a basic notion for the first part\, ”the convolutio
n should be as smooth as the scale allows”\, and ran into fun classical
Fourier Analysis that seems to be new: (a) new uncertainty principles for
the Fourier transform\, (b) that potentially have the characteristic funct
ion as an extremizer\, (c) which leads to strange new patterns in hypergeo
metric functions and (d) produces curious local stability inequalities. No
ah Kravitz and I managed to solve two specific instances on the discrete l
attice completely\, this results in some sharp weighted estimates for poly
nomials on the unit interval – both the Dirichlet and the Fejer kernel m
ake an appearance. The entire talk will be completely classical Harmonic A
nalysis\, there are lots and lots of open problems.\n
LOCATION:https://researchseminars.org/talk/HAeS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Bennett (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20211103T170000Z
DTEND;VALUE=DATE-TIME:20211103T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/22
DESCRIPTION:Title: Th
e nonlinear Brascamp-Lieb inequality and applications\nby Jonathan Ben
nett (University of Birmingham) as part of Harmonic analysis e-seminars\n\
n\nAbstract\nThe Brascamp-Lieb inequality is a broad generalisation of man
y well-known multilinear inequalities in analysis\, including the multilin
ear Hölder\, Loomis-Whitney and sharp Young convolution inequalities. The
re is by now a rich theory surrounding this classical inequality\, along w
ith applications in convex geometry\, harmonic analysis\, partial differen
tial equations\, number theory and beyond. In this talk we present a certa
in nonlinear variant of the Brascamp-Lieb inequality\, placing particular
emphasis on some of its applications. Most of this is joint work with Stef
an Buschenhenke\, Neal Bez\, Michael Cowling and Taryn Flock.\n
LOCATION:https://researchseminars.org/talk/HAeS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Carbery (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20211201T170000Z
DTEND;VALUE=DATE-TIME:20211201T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/23
DESCRIPTION:Title: Du
ality for joints and multijoints - what is it\, what are they\, and why do
we care?\nby Anthony Carbery (University of Edinburgh) as part of Har
monic analysis e-seminars\n\n\nAbstract\nWe discuss theories of duality wh
ich are applicable to the multijoint and joint problems\, which are themse
lves discrete formulations of multilinear and linear Kakeya problems. This
is joint work in part with Timo Hanninen and Stefan Valdimarsson\, and in
part with Michael Tang.\n
LOCATION:https://researchseminars.org/talk/HAeS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Dragičević (University of Ljubljana)
DTSTART;VALUE=DATE-TIME:20211215T170000Z
DTEND;VALUE=DATE-TIME:20211215T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/24
DESCRIPTION:Title: $L
^p$ asymptotics for powers of the complex Riesz transform\nby Oliver D
ragičević (University of Ljubljana) as part of Harmonic analysis e-semin
ars\n\n\nAbstract\nWe establish the sharp behaviour of the $L^p$ norms of
integer powers of the planar Riesz transform $R_2+iR_1$\, and briefly disc
uss the estimates on $L^1$ and $L^\\infty$. This is a joint work with Andr
ea Carbonaro and Vjekoslav Kovač.\n
LOCATION:https://researchseminars.org/talk/HAeS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Philippe Anker (Université d’Orléans)
DTSTART;VALUE=DATE-TIME:20220112T170000Z
DTEND;VALUE=DATE-TIME:20220112T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/25
DESCRIPTION:Title: Di
spersive PDE on noncompact symmetric spaces\nby Jean-Philippe Anker (U
niversité d’Orléans) as part of Harmonic analysis e-seminars\n\n\nAbst
ract\nWe consider the wave equation and the Schrödinger equation on gener
al symmetric spaces of the noncompact type\, which is an interesting class
of Riemannian manifolds with nonpositive curvature\, including all hyperb
olic spaces. The standard strategy consists in establishing first pointwis
e kernel estimates for the fundamental solutions\, in deducing next disper
sive and Strichartz inequalities for the linear equations\, and in applyin
g them finally to semilinearities. This program was successfully achieved
for various classes of manifolds over the past 40 years\, in particular fo
r hyperbolic spaces 10-15 years ago. We were recently able to extend it to
symmetric spaces of higher rank\, in collaboration with V. Pierfelice\, S
. Meda\, M. Vallarino and H.-W. Zhang. In this talk\, we shall report on t
hese progresses\, emphasizing on the tools used to tackle the higher rank
case.\n
LOCATION:https://researchseminars.org/talk/HAeS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malabika Pramanik (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20220126T170000Z
DTEND;VALUE=DATE-TIME:20220126T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/26
DESCRIPTION:Title: On
projections and circles\nby Malabika Pramanik (University of British
Columbia) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThis will
be a survey of two classes of problems in analysis: measuring the size o
f projections of sets\, and incidences of circles in the plane. I will dis
cuss some landmark results and recently discovered connections between the
two.\n
LOCATION:https://researchseminars.org/talk/HAeS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Hickman (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20220209T170000Z
DTEND;VALUE=DATE-TIME:20220209T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/27
DESCRIPTION:Title: Ka
keya maximal estimates via real algebraic geometry\nby Jonathan Hickma
n (University of Edinburgh) as part of Harmonic analysis e-seminars\n\n\nA
bstract\nThe Kakeya (maximal) conjecture concerns how collections of long\
, thin tubes which point in different directions can overlap. Such geometr
ic problems underpin the behaviour of various important oscillatory integr
al operators and\, consequently\, understanding the Kakeya conjecture is a
vital step towards many central problems in harmonic analysis. In this ta
lk I will discuss work with K. Rogers and R. Zhang which apply tools from
the theory of semialgebraic sets to yield new partial results on the Kakey
a conjecture. Also\, more recent work with J. Zahl has used these methods
to improve the range of estimates on the Fourier restriction conjecture.\n
LOCATION:https://researchseminars.org/talk/HAeS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Soria (Universidad Autónoma de Madrid)
DTSTART;VALUE=DATE-TIME:20220223T170000Z
DTEND;VALUE=DATE-TIME:20220223T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/28
DESCRIPTION:Title: In
tegro-differential operators and nonlocal diffusion\nby Fernando Soria
(Universidad Autónoma de Madrid) as part of Harmonic analysis e-seminars
\n\n\nAbstract\nBy a nonlocal diffusion equation we mean an evolution prob
lem where the un-\nknown function is not just reverting to its infinitesim
al average\, but instead it\n\nis influenced by its values at many scales.
It is still a diffusion\, but trying to\nrevert now to an integral averag
e of its surrounding values.\nTypical examples in probability arise when c
onsidering jump (Levy) processes\nin optimal control\, game theory and fin
ance. The quasi-geostrophic equation\nfor ocean-atmosphere interaction pro
vides a ’simple’ model in fluid dynamics.\n\nIn this talk we will pres
ent a\, by no means exhaustive\, survey describing how\nthis theory has ev
olved in recent years.\n
LOCATION:https://researchseminars.org/talk/HAeS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Iliopoulou (University of Kent)
DTSTART;VALUE=DATE-TIME:20220309T170000Z
DTEND;VALUE=DATE-TIME:20220309T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/29
DESCRIPTION:Title: So
me remarks on the Mizohata-Takeuchi conjecture\nby Marina Iliopoulou (
University of Kent) as part of Harmonic analysis e-seminars\n\n\nAbstract\
nThis is a conjecture on weighted estimates for the classical Fourier exte
nsion operators of harmonic analysis. In particular\, let E be the extensi
on operator associated to some surface\, and f be a function on that surfa
ce. If we 'erase' part of Ef\, how well can we control the 2-norm of the r
emaining piece? The Mizohata-Takeuchi conjecture claims some remarkable co
ntrol on this quantity\, involving the X-ray transform of the part of the
support of Ef that we kept. In this talk we will discuss the history of th
e problem\, and will describe a new perspective that modestly improves our
knowledge (for a certain class of weights). This is joint work with A. Ca
rbery.\n
LOCATION:https://researchseminars.org/talk/HAeS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Detlef Müller (University of Kiel)
DTSTART;VALUE=DATE-TIME:20220323T170000Z
DTEND;VALUE=DATE-TIME:20220323T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/30
DESCRIPTION:Title: On
Fourier restriction to hyperbolic 2-surfaces: robustness of the polynomia
l compared to the bilinear approach\nby Detlef Müller (University of
Kiel) as part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk
\, which will be based on joint research with S. Buschenhenke\nand A.Varga
s\, I intend to discuss some of the new challenges that arose in our\nstud
ies of Fourier restriction estimates for hyperbolic surfaces\, compared to
\nthe case of elliptic surfaces. Given the complexity of the bilinear\, an
d even\nmore so of the polynomial partitioning approach\, I shall mainly f
ocus on\nthose parts of these methods which required new ideas\, so that a
familiarity\nwith these methods will not be expected from the audience.\n
LOCATION:https://researchseminars.org/talk/HAeS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carmelo Puliatti (Euskal Herriko Unibertsitatea)
DTSTART;VALUE=DATE-TIME:20220413T160000Z
DTEND;VALUE=DATE-TIME:20220413T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/31
DESCRIPTION:Title: Gr
adients of single layer potentials for elliptic operators with coefficient
s of Dini mean oscillation-type\nby Carmelo Puliatti (Euskal Herriko U
nibertsitatea) as part of Harmonic analysis e-seminars\n\n\nAbstract\nWe c
onsider a uniformly elliptic operator $L_A$ in divergence form \nassociate
d with a matrix $A$ with real\, bounded\, and possibly \nnon-symmetric coe
fficients. If a proper $L^1$-mean oscillation of the \ncoefficients of $A$
satisfies suitable Dini-type assumptions\, we prove \nthe following: if $
\\mu$ is a compactly supported Radon measure in \n$R^{n+1}\, n\\geq 2\,$
the $L^2(\\mu)$-operator norm of the gradient of the \nsingle layer potent
ial $T_\\mu$ associated with $L_A$ is comparable to the \n$L^2$-norm of th
e $n$-dimensional Riesz transform $R_\\mu$\, modulo an \nadditive constant
.\nThis makes possible to obtain direct generalizations of some deep \ngeo
metric results\, initially proved for the Riesz transform\, which \nwere r
ecently extended to $T_\\mu$ under a H\\"older continuity assumption \non
the coefficients of the matrix $A$.\n\nThis is a joint work with Alejandro
Molero\, Mihalis Mourgoglou\, and \nXavier Tolsa.\n
LOCATION:https://researchseminars.org/talk/HAeS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Saliani (Università degli Studi della Basilicata)
DTSTART;VALUE=DATE-TIME:20220420T160000Z
DTEND;VALUE=DATE-TIME:20220420T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/32
DESCRIPTION:Title: Sp
ectral graph transforms: wavelets\, frames\, and open problems\nby San
dra Saliani (Università degli Studi della Basilicata) as part of Harmonic
analysis e-seminars\n\n\nAbstract\nClassical transforms\, as Fourier\, wa
velet\, wavelet packets and time-frequency dictionaries have been general
ized to functions defined on finite\, undirected graphs\, where the connec
tions between vertices are encoded by the Laplacian matrix.\n\nDespite wor
king in a finite and discrete environment\, many problems arise in applica
tions where the graph is very large\, as it is not possible to determine a
ll the eigenvectors of the Laplacian explicitly. For example\, in the case
of our interest: a voxel-wise brain graph $\\mathcal{G}$ with $900760$ no
des (representing the brain voxels)\, and signals given by the fRMI (funct
ional magnetic resonance imaging).\n\nAfter an overview of the methods and
of the open problems\, we present a new method to generate frames of wav
elet packets defined in the graph spectral domain to represent signals on
finite graphs.\n\n\nJoint work with Iulia Martina Bulai.\n
LOCATION:https://researchseminars.org/talk/HAeS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Bramati (Ghent University)
DTSTART;VALUE=DATE-TIME:20220518T160000Z
DTEND;VALUE=DATE-TIME:20220518T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/33
DESCRIPTION:Title: Re
sonances of invariant differential operators\nby Roberto Bramati (Ghen
t University) as part of Harmonic analysis e-seminars\n\n\nAbstract\nGiven
a self-adjoint differential operator with continuous spectrum acting on a
Hilbert space H\, its resonances are the poles of a meromorphic extension
across the spectrum of its resolvent acting on a dense subspace of H in w
hich the operator is no longer self-adjoint. They can be thought of as rep
lacements of eigenvalues for problems on noncompact domains. In this talk
we will first explore two well-understood cases: the Laplacian on Euclidea
n spaces and the Laplace-Beltrami operator on rank one Riemannian symmetri
c spaces of the noncompact type\, two settings where a notion of Fourier a
nalysis is available. In both cases\, the Laplacian comes from the action
of the Casimir operator through the left regular representation of the und
erlying group\, and the Plancherel formula provides a direct integral deco
mposition of such representation. Elaborating from this point of view\, in
collaboration with A. Pasquale and T. Przebinda we started to develop met
hods to study resonances in more general settings. As an example of such m
ethods\, in the talk we will consider some instances of Capelli operators
and see how one can exploit Howe’s theory for reductive dual pairs. We w
ill also consider the problem of identifying the representations that are
naturally attached to the resonances in these settings.\n
LOCATION:https://researchseminars.org/talk/HAeS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Vitturi (University College Cork)
DTSTART;VALUE=DATE-TIME:20220615T160000Z
DTEND;VALUE=DATE-TIME:20220615T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/34
DESCRIPTION:Title: A
restricted 2-plane transform related to Fourier Restriction in codimension
2\nby Marco Vitturi (University College Cork) as part of Harmonic ana
lysis e-seminars\n\n\nAbstract\nThe $2-$plane transform is the operator th
at maps a function to its averages along affine $2-$planes. We consider th
e operator obtained by restricting the allowed directions of the $2-$plane
s to those normal to a fixed surface $S$ (quadratic\, for simplicity) of c
odimension $2$. By duality and discretisation\, $L^p\\to L^q$ estimates fo
r such an operator imply Kakeya-type estimates for the supports of Fourier
-transformed wave-packets adapted to the surface $S$ (wave-packet decompos
itions being a powerful tool in proving Fourier Restriction results). We c
onnect this operator to Gressman's theory of affine invariant measures by
showing that if the surface is well-curved à la Gressman (meaning\, the a
ffine invariant surface measure on S is non-vanishing) then the restricted
$2-$plane transform is $L^p\\to L^q$ bounded in the maximal range of $(p\
,q)$ exponents allowed. The proof relies on a characterisation of well-cur
vedness in Geometric Invariant Theory terms\, which will be discussed.\nJo
int work with S. Dendrinos and A. Mustata.\n
LOCATION:https://researchseminars.org/talk/HAeS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinai Robins (Universidade de São Paulo)
DTSTART;VALUE=DATE-TIME:20220629T160000Z
DTEND;VALUE=DATE-TIME:20220629T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/35
DESCRIPTION:Title: Th
e covariogram and extensions of the Bombieri-Siegel formula\nby Sinai
Robins (Universidade de São Paulo) as part of Harmonic analysis e-semina
rs\n\n\nAbstract\nWe extend a formula of C. L. Siegel in the geometry of n
umbers\, allowing the body to contain an arbitrary number of interior latt
ice points. Our extension involves a lattice sum of the cross covariogram
for any two bounded sets $A\, B\\subseteq \\mathbb R^d$\, and turns out to
also extend a\nresult of E. Bombieri. We begin with a new variation of th
e Poisson summation formula\, which may be of independent interest. One of
the consequences of these results is a new characterization of multitilin
gs of Euclidean space by translations\, which is an application of Bombier
i’s identity and of our extension of it. Some classical results\, such a
s Van der Corput’s inequality\, and Hardy’s identity for the Gauss cir
cle problem\, also follow as corollaries. This is joint work with Michel F
aleiros Martins.\n
LOCATION:https://researchseminars.org/talk/HAeS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izabella Łaba (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20221005T160000Z
DTEND;VALUE=DATE-TIME:20221005T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/36
DESCRIPTION:Title: Fa
vard length estimates via cyclotomic divisibility\nby Izabella Łaba (
University of British Columbia) as part of Harmonic analysis e-seminars\n\
n\nAbstract\nThe Favard length of a planar set $E$ is the average length o
f its one-dimensional projections. It is well known (due to Besicovitch) t
hat if $E$ is a purely unrectifiable planar self-similar set of Hausdorff
dimension 1\, then its Favard length is 0. Consequently\, if $E_\\delta$ i
s the $\\delta$-neighbourhood of $E$\, then the Favard length of $E_\\delt
a$ goes to 0 as $\\delta\\to 0$. A question of interest in geometric measu
re theory\, ergodic theory and analytic function theory is to estimate the
rate of decay\, both from above and below. Partial results in this direct
ion have been proved by many authors\, including Mattila\, Nazarov\, Perez
\, Volberg\, Bond\, Bateman\, and myself. In addition to geometric measure
theory\, this work has involved methods from harmonic analysis\, additive
combinatorics\, and algebraic number theory. I will review the relevant b
ackground\, and then discuss my recent work with Caleb Marshall on upper b
ounds on the Favard length for 1-dimensional planar Cantor sets with a rat
ional product structure. This improves on my earlier work with Bond and Vo
lberg\, and incorporates new methods introduced in my work with Itay Londn
er on integer tilings.\n
LOCATION:https://researchseminars.org/talk/HAeS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford University - NTNU)
DTSTART;VALUE=DATE-TIME:20221019T160000Z
DTEND;VALUE=DATE-TIME:20221019T170000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/37
DESCRIPTION:Title: So
me inequalities for Laplace eigenfunctions and their gradients\nby Eug
enia Malinnikova (Stanford University - NTNU) as part of Harmonic analysi
s e-seminars\n\n\nAbstract\nWe will survey some recent results on restrict
ions of Laplace eigenfunctions\nand present new norm inequalities for the
eigenfunctions and their gradients\nobtained in a joint work with Stefano
Decio. The guiding principle\, which\ngoes back to the works of Donnelly a
nd Fefferman\, is that eigenfunctions with\neigenvalue $\\textrm{E}^2$ beh
ave like (harmonic) polynomials of degree $\\textrm{E}$.\n
LOCATION:https://researchseminars.org/talk/HAeS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giancarlo Travaglini (University of Milano-Bicocca)
DTSTART;VALUE=DATE-TIME:20221116T170000Z
DTEND;VALUE=DATE-TIME:20221116T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/38
DESCRIPTION:Title: Ir
regularities of distribution\nby Giancarlo Travaglini (University of M
ilano-Bicocca) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe
term “Irregularities of distribution” appeared for the first time in t
he title of 1954 K. Roth’s seminal paper and referred to a conjecture of
J. van der Corput on the non-existence of a “good” way to choose an
infinite sequence in the unit interval. Roth approached van der Corput’s
conjecture by checking the quality of any choice of N points in the 2-dim
ensional torus with respect to arbitrary squares therein\, and proving a l
ogarithmic lower bound for the discrepancy. Later W. Schmidt\, H. Montgome
ry and J. Beck independently proved that the discrepancy is at least a pow
er of N when squares are replaced with disks. \n\nWe construct a family of
intermediate cases and we show that positive curvature plays no role in t
his problem which reduces to a careful study of the decay of certain Fouri
er transforms.\n\nWe shall also describe two related d-dimensional problem
s. \n\n(from joint works with Luca Brandolini and Leonardo Colzani)\n
LOCATION:https://researchseminars.org/talk/HAeS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajula Srivastava (University of Bonn - Max Planck Institute for M
athematics)
DTSTART;VALUE=DATE-TIME:20230111T170000Z
DTEND;VALUE=DATE-TIME:20230111T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/39
DESCRIPTION:Title: Th
e Korányi Spherical Maximal Function on Heisenberg groups\nby Rajula
Srivastava (University of Bonn - Max Planck Institute for Mathematics) as
part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk\, we disc
uss the problem of obtaining sharp $L^p \\to L^q$ estimates for the local
maximal operator associated with averaging over dilates of the Korányi sp
here on Heisenberg groups. This is a codimension one surface compatible wi
th the non-isotropic Heisenberg dilation structure. I will describe the ma
in features of the problem\, some of which are helpful while others are ob
structive. These include the non-Euclidean group structure (the extra “t
wist” due to the Heisenberg group law)\, the geometry of the Korányi sp
here (in particular\, the flatness at the poles) and an “imbalanced” s
caling argument encapsulated by a new type of Knapp example\, which we sha
ll describe in detail.\n
LOCATION:https://researchseminars.org/talk/HAeS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (University of Valencia)
DTSTART;VALUE=DATE-TIME:20230125T170000Z
DTEND;VALUE=DATE-TIME:20230125T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T213716Z
UID:HAeS/40
DESCRIPTION:Title: En
dpoint sparse domination for oscillatory Fourier multipliers\nby David
Beltran (University of Valencia) as part of Harmonic analysis e-seminars\
n\n\nAbstract\nSparse domination was first introduced in the context of Ca
lderón--Zygmund theory. Shortly after\, the concept was successfully exte
nded to many other operators in Harmonic Analysis\, although many endpoint
situations have remained unknown. In this talk\, we will present new endp
oint sparse bounds for oscillatory and Miyachi-type Fourier multipliers us
ing Littlewood--Paley theory. Furthermore\, the results can be extended to
more general dilation-invariant classes of multiplier transformations via
Hardy space techniques\, yielding results\, for instance\, for multi-scal
e sums of radial bump multipliers.\n
LOCATION:https://researchseminars.org/talk/HAeS/40/
END:VEVENT
END:VCALENDAR