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

Abstract

Let L be a non-negative self-adjoint operator acting on L2(Rn) satisfying a pointwise Gaussian estimate for its heat kernel. Let w be an Ap weight on Rn×Rn, 1<p<∞. In this article we obtain a weighted q-atomic decomposition with q≥p for the weighted Hardy space HL,w1(Rn×Rn) associated to L.