| Though the theory of one-parameter Triebel-Lizorkin and Besov spaces hasbeen made great progress, the multi-parameter counterpart of such a theory isstill vacant. We gave the definition of multi-parameter weighted Triebel-Lizorkinand Besov spaces and discussed the boundedness problem of multi-parameterCalder′on-Zygmund operator in such spaces. The main purpose of this paper is todevelop a theory of multi-parameter weighted Triebel-Lizorkin and Besov spacesby using the discrete weighted Littlewood-Paley-Stein analysis in the setting ofimplicit multi-parameter structure.In the second chapter, we proved the minimal-maximal comparison theoremin multi-parameter weighted Triebel-Lizorkin and Besov spaces by the applicationof standardized estimates, Fe?erman-Stein vector inequality and Holder inequality.Finally, through the discrete Caldero′n reproducing formula and orthogonality es-timates, we gave the characterization of discrete Littlewood-Paley-Stein in Triebel-Lizorkin and Besov spaces. We also proved the boundedness of singular integraloperators on multi- parameter weighted Triebel-Lizorkin and Besov spaces. |
