Boundedness Of Some Operators On Herz-Morrey Spaces With Variable Exponents

Multilinear operators are a class of important operators in the field of harmonic analysis.Since multilinear operators are a very important tool in solving the boundedness problems of some difficult nonlinear operators,they have been researched extensively.In addition,Hardy operators and sublinear operators are classic operators in harmonic analysis,they have important applications in partial differential equations and other disciplines.On the basis of the above background,this dissertation mainly studies the bounded problems of bilinear Hardy operators,bilinear Calderón-Zygmund operators and sublinear operators on the variable exponents Herz-Morrey spaces.This dissertation firstly gives the boundedness of bilinear commutators generated by bilinear Hardy operators and BMO functions on products of Herz-Morrey spaces with variable exponents and products of weighted Herz-Morrey spaces with variable exponents.Secondly,the boundedness of the bilinear Calderón-Zygmund operators on weighted Herz-Morrey spaces with variable exponents and vector valued bilinear Calderón-Zygmund operators on products of weighted Herz-Morrey spaces with variable exponents are given.Finally,the boundedness of vector valued sublinear operators on weighted Herz-Morrey spaces with variable exponents is obtained.