Dimension-free $L^p$ estimates for vectors of Riesz transforms in the rational Dunkl setting

TL;DR

This paper establishes dimension-free $L^p$ bounds for Riesz transforms in the rational Dunkl setting using a Bellman function approach, advancing harmonic analysis in this context.

Contribution

It introduces a novel application of the Bellman function method to obtain dimension-free estimates for Riesz transforms in the Dunkl setting.

Findings

Proved dimension-free $L^p$ bounds for Riesz transforms in the Dunkl setting.

Applied Bellman function technique to harmonic analysis problems.

Extended the understanding of Riesz transforms beyond classical Euclidean spaces.

Abstract

In this article, we prove dimension-free upper bound for the $L^p$-norms of the vector of Riesz transforms in the rational Dunkl setting. Our main technique is Bellman function method adapted to the Dunkl setting.