ATOMIC DECOMPOSITION FOR WEIGHTED H^p SPACES ON PRODUCT DOMAINS

By using the weighted versions of Journe's covering lemma and its extension to highetdimensions, this paper contributes an atomic decomposition theorem for the weighted H^p(0<p≤1)spaces on product domains, gets a vector value for the index of the moment conditions whichextends the corresponding result in the case with one--parameter to the case with arbitrarynumber of parameters and solves the problem proposed by S. Y. A. Chang &R. Fefferman.

By using the weighted versions of Journe’s covering lemma and its extension to highetdimensions, this paper contributes an atomic decomposition theorem for the weighted H^p(0&lt;p≤1)spaces on product domains, gets a vector value for the index of the moment conditions whichextends the corresponding result in the case with one--parameter to the case with arbitrarynumber of parameters and solves the problem proposed by S. Y. A. Chang &R. Fefferman.