Riesz Transforms Characterizations of Hardy Spaces $$H^1$$ for the Rational Dunkl Setting and Multidimensional Bessel Operators

We characterize the Hardy space (H^1) in the rational Dunkl setting associated with the reflection group (mathbb {Z}_2^n) by means of special Riesz transforms. As a corollary we obtain Riesz transforms characterization of (H^1) for product of Bessel operators in ((0,infty )^n).