Room P3.10, Mathematics BuildingOnline Instituto Superior Técnico

Joris Roos

Joris Roos, University of Edinburgh
Spherical maximal functions and fractal dimensions of dilation sets

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.