Boundedness Of Higher Order Commutators With Rough Kernels On The Weighted Herz-Morrey Spaces

It is well known that the homogeneous type Herz space is a very important function space in the harmonic analysis. We have been well known about the estimates for some operators on the homogeneous spaces, the homogeneous type Herz-Morrey space is a new function spaces which is introduced during the study of multi-harmonic analysis in recent years. We know that the Herz spaces are generalization of LP space, and the homogeneous type Herz-Morrey space is generalization of the homogeneous type Herz space, they have the following relationsMoreover, people have now paid more attention to the boundedness of commutators(see[1] [2][3][4][5]).This thesis aims to study the boundedness of higher order commutators Mb,m,Ω, Tb,m gen-erated by some operators with rough kernels and BMO functions on the weighted Herz-Morrey Space.The thesis comprises there chapters.In chapter 1, we present the background and give some necessary notations as well as definitions of spaces.In chapter 2, we estimate the boundedness of higher order commutators Mb,m,Ω, Tb,m generated by Mm,Ω, Tm and BMO function on the weighted Herz-Morrey Space.In chapter 3, we estimate the boundedness of the higher order commutators Tb,lm and Mb,lm generated by fractional integral operators Tl and maximal fractional operators Ml and BMO(Rn)function on the weighted Herz-Morrey space.