Riesz Transform Characterizations for Multidimensional Hardy Spaces

We study Hardy space H-L(1)(X) related to a self-adjoint operator L defined on an Euclidean subspace X of R-d. We continue study from [27], where, under certain assumptions on the heat semigroup exp( -t L), the atomic characterization of local type for H-L(1 )(X) was proved. In this paper we provide additional assumptions that lead to another characterization of H-L(1)(X) by the Riesz transforms related to L. As an application, we prove the Riesz transform characterization of H-L(1)(X) for multidimensional Bessel and Laguerre operators, and the Dirichlet Laplacian on R-+(d).