Riesz transforms characterizations of Hardy spaces $H^1$ for the rational Dunkl setting and multidimensional Bessel operators

TL;DR

This paper characterizes Hardy spaces $H^1$ in the rational Dunkl setting using Riesz transforms, extending the understanding of these spaces in relation to Bessel operators in multiple dimensions.

Contribution

It provides the first Riesz transform characterization of $H^1$ in the rational Dunkl setting and for products of Bessel operators in higher dimensions.

Findings

Hardy space $H^1$ characterized via Riesz transforms in Dunkl setting

Extension of $H^1$ characterization to multidimensional Bessel operators

New tools for analysis in reflection group-invariant contexts

Abstract

We characterize the Hardy space $H^1$ in the rational Dunkl setting associated with the reflection group $\mathbb Z_2^n$ by means of Riesz transforms. As a corollary we obtain a Riesz transform characterization of $H^1$ for product of Bessel operators in $(0,\infty)^n$.