WEIGHTED HARDY SPACES ASSOCIATED TO SELF-ADJOINT OPERATORS AND BMOL,w

Let L be a non-negative self-adjoint operator satisfying a pointwise Guassian estimate for its heat kernel. Let w be some A(s), weight on R-n. In this paper, we obtain a weighted (p, q)-atomic decomposition with q >= s for the weighted Hardy spaces.H-L,w(p)(R-n), 0 < p <= 1. We also introduce the suitable weighted BMO spaces BMOL,wP. Then the duality between H-L,w(1)(R-n) and BMOL,w is established.