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 integral operator on L? space to Bloch space on the unit ball.Second,we study the weighted differentiation composition operator from Besov space into Bloch type space on the unit disk.This paper is divided into five chapters.The first chapter is the introduction of the whole paper.In this part,we briefly describes the research background,some recent results about the the integral operator and weighted differentiation composition operator which are contained in this paper,and the main results about this paper.The second chapter is some prior knowledge section.In this part,we mainly introduce some basic notations and properties which will be used in the later part of this paper.This section induces some related contents about complex analysis,the theory of function spaces,.real analysis,geometric function theory and operator theory.In the third chapter,we study the integral operators Pt? from L?(Bn)spaces to Bloch type spaces Ba on the unit ball.This chapter is the generalization of the results in the reference[12],and gives the norm of integral operators Pt? from L?(Bn)spaces to Bloch type spaces B? on the unit ball.The fourth chaper mainly gives the sufficient and necessary conditions for the boundedness and compactness of the weighted differentiation composition operators D?n,u from Besov spaces Bp,q to Bloch type spaces Ba on the unit disk.In the fifth chapter,we summarize the thesis briefly.