# Błażej Wróbel: Dimension-free estimates for Hardy-Littlewood maximal functions in discrete contexts

Title: Dimension-free estimates for Hardy-Littlewood maximal functions in discrete contexts.

Abstract: The topic of dimension-free Lp estimates for Hardy Littlewood maximal functions over convex bodies in Rd had been mainly developed in the '80 and '90 in the work of Stein, Bourgain, Carbery, and Müller. The interest in the topic has been recently renewed due to recent progress by Aldaz 2011 and Bourgain 2014.

Last year, together with J. Bourgain, M. Mirek, and E.M. Stein, we initiated the study of dimension-free bounds for maximal functions in discrete contexts, i.e. with Rd replaced by Zd. In this talk I am going to give an overview of the results we obtained. In particular I will present a positive result for the discrete cubes and the discrete Euclidean balls.

The talk is based on joint work with J. Bourgain, M. Mirek, and E.M. Stein.

Seminar bo v predavalnici 3.06 na Jadranski 21. Vljudno vabljeni!

Vodji seminarja

Franc Forstnerič in Barbara Drinovec Drnovšek