Research On Boundedness Of Commutators Of Some Operators On Spaces With Variable Exponent

In this thesis, we mainly study the boundedness of some operators and their commutators in spaces with variable exponent. It consists of four chapters.In the first chapter, we mainly introduce the background knowledge involved in this paper and give some necessary concepts and lemmas at the same time.In the second chapter, we mainly discuss the boundedness of higher order com-mutators on Herz-Morrey spaces with variable exponent.In the third chapter, we consider the boundedness of multilinear fractional inte-gral operators on products of Lebesgue spaces and Herz spaces with variable exponent. Moreover, the boundedness of its commutators on products of Herz spaces with vari-able exponent are obtained.In the fourth chapter, we mainly talk about the boundedness of commutators on Morrey spaces with variable exponent.