A maximal function characterization for Hardy spaces associated to nonnegative self-adjoint operators satisfying Gaussian estimates

Let L be a nonnegative, self-adjoint operator satisfying Gaussian estimates on L-2 (R-n). In this article we give an atomic decomposition for the Hardy spaces H-L,max(p) (R-n) in terms of the nontangential maximal functions associated with the heat semigroup of L, and this leads eventually to characterizations of Hardy spaces associated to L, via atomic decomposition or the nontangential maximal functions. The proof is based on a modification of a technique due to A. Calderon [6]. (C) 2015 Elsevier Inc. All rights reserved.