The atomic decomposition of weighted Hardy spaces associated to self-adjoint operators on product spaces

Let L be a non-negative self-adjoint operator acting on L-2(R-n) satisfying a pointwise Gaussian estimate for its heat kernel. Let w be an A(p) weight on R-n x R-n, 1 < p < infinity. In this article we obtain a weighted q-atomic decomposition with q >= p for the weighted Hardy space H-L,w(1)(R-n x R-n) associated to L. (C) 2016 Elsevier Inc. All rights reserved.