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

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 $(0,\infty {)}^n$.