Riesz transform characterizations for multidimensional Hardy spaces

Abstract

We study Hardy space $H_L^1(X)$ related to a self-adjoint operator $L$ defined on Euclidean domain $X\subseteq {\mathbb{R}}^d$. Under certain assumptions on the heat semigroup $\exp (-tL)$ we prove characterization of $H_L^1(X)$ by the Riesz transforms related to $L$. As an application, we prove the Riesz transform characterization for multidimensional Bessel and Laguerre operators.