Boundedness Of A Class Of Operators On Function Space

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 Hardy space.Second,we study the weighted differential composition operators onto little Bloch-type spaces on the unit disk.This paper is divided into four chapters.Chapter 1 is the introduction.We briefly introduce the research significance?research status and the main research content of this paper.In chapter 2,we prove the necessary and sufficient conditions for the singular integral operator K from Za spaces into H?(D)spaces?from LP(D)spaces into Za spaces and from Hp(D)spaces into Z?spaces.In chapter 3,we prove the boundedness and compactness of weighted differentiation composition operators D?,un from ?0? onto B0?on the unit disk,and the boundedness and compactness of weighted differentiation composition operators D?,un from B?(B0?)onto B?(B0?)were characterized in two aspects,weight functions ?,u and index?,? respectively.In chapter 4,we summarize the thesis briefly.