# Mathematical Sciences Research Institute

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# Jump inequalities for translation-invariant polynomial averages and singular integrals on $\mathbb Z^d$

## Recent Developments in Harmonic Analysis May 15, 2017 - May 19, 2017

May 15, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Mariusz Mirek (Hausdorff Research Institute for Mathematics, University of Bonn)
Location: MSRI: Simons Auditorium
Tags/Keywords
• harmonic analysis

• singular integrals

• discrete Radon transform

• number theory

• variational estimates

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### Mirek

Abstract

The aim of this talk is to prove $\ell^p(\mathbb Z^d)$ inequalities with $1 < p < \infty$, for $\lambda$-jumps for discrete Radon transforms. These inequalities are the $r = 2$ endpoints of the $r$-variational estimates due to Mirek, Stein, and Trojan. This is a joint project with E.M. Stein and P. Zorin-Kranich.

Supplements