Averages along polynomial sequences in discrete nilpotent groups: singular Radon transforms

TL;DR

This paper proves the $L^2$ boundedness of discrete singular Radon transforms along polynomial sequences in step 2 nilpotent groups, advancing understanding of harmonic analysis in non-commutative discrete settings.

Contribution

It establishes the first $L^2$ boundedness results for these transforms in the context of discrete nilpotent groups of step 2, extending classical harmonic analysis techniques.

Findings

Proved $L^2$ boundedness of singular Radon transforms in step 2 nilpotent groups.

Extended harmonic analysis methods to non-commutative discrete groups.

Provided a framework for analyzing polynomial averages in discrete nilpotent groups.

Abstract

We consider a class of operators defined by taking averages along polynomial sequences in discrete nilpotent groups. In this paper we prove $L^2$ boundedness of discrete singular Radon transforms along general polynomial sequences in discrete nilpotent groups of step 2.