Singular Integral Operators And Weighted Composition Operators On Function Spaces

The main content of this thesis is divided into two parts.First,we study the singular integral operators induced by the reproducing kernel of the Drury-Arveson space.Second,we study the weighted composition operators from Besov spaces into the Zygmund spaces on the unit disk.This paper is divided into four chapters.Chapter 1 is the introduction.We briefly introduce the research significance and research status,and then introduce the main research content of this paper.In chapter 2,we give the necessary and sufficient conditions for the singular integral operator K from LP(Bn)spaces into Hn2 space and from Lp(Bn)spaces into Lq(Bn)spaces.Then we give the relevant proof.In chapter 3,we give the the sufficient and necessary condition for uC? to be bounded and compact operators from Bp,q to Z,and then give the relevant proof.In chapter 4,we summarize the thesis briefly.