Lisbon Webinar in Analysis and Differential Equations

Spherical maximal functions and fractal dimensions of dilation sets

Sala P3.10, Instituto Superior Técnico (com transmissão via Zoom)

Por Joris Roos (University of Edinburgh).

In this talk we will consider spherical maximal operators in Euclidean space with a supremum taken over a given dilation set. It turns out that the sharp $L^p$ improving properties of such operators are closely related to fractal dimensions of the dilation set such as the Minkowski and Assouad dimensions.

At the center of the talk will be a simple characterization of the closed convex sets which can occur as closure of the sharp $L^p$ improving region of such a maximal operator.

This is joint work with Andreas Seeger. Time permitting, we will also discuss some ongoing work and further directions.

Transmissão via Zoom (pw: lisbonwade).

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.