Lp improving bounds for spherical maximal operators

Abstract: Consider maximal operators for spherical means where the dilations are

restricted to a given subset of a compact interval. We discuss Lp improving

estimates for such operators and connections to related global problems.

The results depend on various notions of fractal dimension of the dilation

set or subsets of it. There are some unexpected results on the shape of the

possible type set. This is joint work with Joris Roos, and also relates to earlier work with

Theresa Anderson, Kevin Hughes and Joris Roos.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom