Boundedness Of Vector-valued Calder(?)n-Zygmund Operators On Function Spaces With Variable Exponents

The dissertation is devoted to the boundedness of Calder(?)n-Zygmund operators on function spaces with variable exponents and its application. The plan is the following:In Chapter 1, there are the literature review, definitions, notations and the statement of main results.In Chapter 2, A vector-valued multilinear Calder(?)n-Zygmund operator is proved to be bounded on products of Herz-Morrey spaces with variable exponents.In Chapter 3, it is proved that Banach space valued Calder(?)n-Zygmund operators satisfying operatorvalued (?)ormander's conditions are bounded on Banach space valued Lebesgue spaces with global log(?)older continuous variable exponent over metric measure spaces of homogeneous type. As an application,it is obtained that the boundedness of vector-valued Hardy-Littlewood maximal operator on Lebesgue spaces with global log-(?)older continuous variable exponent over metric measure spaces of homogeneous type.