Composition Operators Between Bloch Type Space And Zygmund Type Space

The theory of composition operators in analytic function spaces is important com-ponent parts in dealing with classical problem of the theory of functions. Currently,many scholars from domestic and foreign are interested in the research of the proper-ties of diferent operators in function spaces and gradually,form series of the theoreticalsystem. I use the methods of functional analysis and several complex variables to solvesome new problems about the properties of compound operators,which the predecessorshave not referred to.This paper mainly characterizes the sufcient and necessary condi-tions for the boundedness and compactness of integral type operators and compositionfollowed by diferentiation between the Bloch type space and the Zygmund type spaceon the unit disk.This paper is mainly divided into four chapters.The first chapter is the introduction of the whole paper.In this part,we main-ly introduce some recent results about some operators which are invovled in this pa-per.Thereafter we will describe the proof in this paper under the basis of existing results.The second chapter is some prior knowledge section. In this part,we mainly intro-duce some basic notations, properties and related lemma.The third chapter mainly gives the sufcient and necessary conditions for theboundedness and compactness of the composition followed by diferentiation CφD fromthe Bαspace to Zμon the unit diskDofC.The fourth chapter mainly gives the sufcient and necessary conditions for bound-edness and compactness of the integral type operator Cnφ,gfrom the Bαspace to Zμonthe unit diskDofC.