Buongiorno a tutti,
annuncio due seminari che si terranno in scuola domani.
A presto,
Alessandra
Tuesday May 23, 10:00 Aula Volterra (Scuola Normale)
Michael Cowling (University of New South Wales)
Title: Hardy spaces in exotic geometries
Abstract: The Heisenberg group appears in complex analysis as the
boundary of a Siegel domain. Study of the boundary values of
holomorphic functions leads to questions in analysis on the Heisenberg
group, equipped with a flag geometry, in which the balls of classical
geometry are replaced by the products of a ball in the sub-Riemannian
geometry and an interval in the central variable.
Flag Hardy spaces are a tool for solving problems in flag geometry;
they present many features in common with Hardy spaces on product
spaces. This talk focusses on the theory of flag Hardy spaces on the
Heisenberg group, and on the difficulties which arise when one tries
to extend to more exotic geometries.
Alessio Martini
(Politecnico di Torino)
Title: A sharp multiplier theorem on solvable extensions of Heisenberg and related groups
Abstract:
Let L be a sub-Laplacian on a sub-Riemannian manifold M. It has been long known that, under fairly general assumptions on L and M,
an
operator of the form F(L) is L^p-bounded (1<p<infinity) whenever the spectral multiplier F satisfies a scale-invariant smoothness condition of sufficiently large order,
related
to the Hausdorff dimension and the volume growth of M.
The
problem of determining the minimal smoothness assumption, however, remains wide open in general.
In
recent years, a number of examples have been discovered where the minimal condition for L^p-boundedness turns out to be related to the topological dimension,
which
is smaller than the Hausdorff dimension when L is not elliptic.
In
joint work with Paweł Plewa (arXiv:2305.03467), we show that this surprising phenomenon also happens on manifolds with exponential volume growth.