ATOMIC DECOMPOSITION FOR WEIGHTED HP SPACES ON PRODUCT DOMAINS

By using the weighted versions of Journe's covering lemma and its extension to higher dimensions, this paper contributes an atomic decomposition theorem for the weighted H(p) (0 < p less-than-or-equal-to 1) spaces on product domains, gets a vector value for the index of the moment conditions which extends the corresponding result in the case with one-parameter to the case with arbitrary number of parameters and solves the problem proposed by S. Y. A. Chang & R. Fefferman[1].