The Boundedness Of Commutators Of Variable Fractional Operators On Variable Exponent Spaces

In the field of harmonic analysis, the boundedness of operator and commutators in various types of function spaces has always been the focus of the study. Recently, the boundedness of the fractional integral operator and it’s commutators in various types of function spaces have received extensive attention. In this paper, we consider the boundedness of commutators of variable fractional integral operators on variable exponent Morrey, Herz, and Herz-Morrey spaces.In the first chapter, we firstly introduce the research background and status of fractional integral operator and Morrey, Herz, Herz-Morrey function spaces. Secondly, we give some necessary notations and lemmas to continue the next three chapters.In the second chapter, using the sharp maximum operator theory, we prove the boundedness of commutators of variable fractional integral operators with BMO functions on Morrey space with variable exponent.For the last two chapters, since the equivalence of α(x) with a(y) in variable fractional integral operators Iα(·), the boundedness of commutators generating by variable fractional integral operators with BMO functions on variable exponent Herz and Herz-Morrey spaces can be obtained.