Mariusz Mirek

Title: Dimension free estimates for the discrete Hardy-Littlewood maximal functions

Abstract: The aim of this talk is to discuss recent developments in dimension-free estimates in harmonic analysis. We show that the discrete Hardy-Littlewood maximal functions associated with the Euclidean balls in $\mathbb Z^d$ with dyadic radii have bounds independent of the dimension on $\ell^p(\mathbb Z^d)$ for every $p\in[2, \infty]$.

This talk is based on joint papers with J. Bourgain, E.M. Stein and B. Wróbel.

Slides