Weighted Inequalities For Certain Fractional Type Integrals And Commutators

In this paper,we study the commutators generated by Lipschitz functions and fractional type integral operators with kernels of the form K?(x,y)?k1(x-A1y)k2(x-A2y)…km(x-Amy),where ?1+…?m=n-?,each ki satisfies the(n-?i)-order fractional size condition and(n-?i)-order generalized fractional Hormander condition,Ai is invertible and Ai-Aj is invertible for i?j,1?i,j?m.This paper is divided into two chapters.Chapter 1 is devoted to the establishment of the corresponding Sharp maximal function estimates for these commutators,and further obtains their weighted Coifman type inequalities,weighted Lp(wp)?Lq(wq)estimates and weighted endpoint estimates.Chapter 2,we study the boundedness of the fractional integral operators and their commutators mentioned above in the weighted Morrey space.With the help of Sharp maximal function estimation,its endpoint estimation is also established.