Bellman Functions and Dimension Free $L^p$estimates for the Riesz Transforms in Bessel settings

TL;DR

This paper proves that Riesz transforms related to Bessel operators are bounded on L^p spaces independently of dimension, providing explicit p-dependent estimates using Bellman functions.

Contribution

It introduces a Bellman function approach to establish dimension-free L^p bounds for Bessel-related Riesz transforms with explicit p-dependence.

Findings

Dimension-free L^p bounds for Bessel-Riesz transforms.

Linear growth of L^p norms with respect to p.

Explicit estimates of the L^p norms in terms of p.

Abstract

In this article we prove dimension free $L^p$-boundedness of Riesz transforms associated with a Bessel diferential operator. We obtain explicit estimates of the $L^p$-norms for the Bessel-Riesz transforms in terms of p, establishing a linear behaviour with respect to p. We use the Bellman function technique to prove a bilinear dimension free inequality involving Poisson semigroups defined through this Bessel operator.