The Boundedness, Compactness And Diference Of The Weighted Composition Operator

In recent years, composition operators in the spaces of the holomorphic functions isa hot issue of the academic. The algebraic structure of composition operators is the mostimportant and difcult problem in the studying of composition operators in the spaces ofthe holomorphic functions. It is significant that we study the boundedness,compactnessand diferences of composition operators in the spaces of the holomorphic functions. Thepaper mainly use the analysis to study the boundedness,compactness and diferences ofthe composition operators in some spaces of the holomorphic functions.This paper is mainly divided into four chapters.The first chapter is mainly about the introduction of the background of this branchand the process we study the composition operators. Thus, give the study of this paper.The second chapter is some priority knowledge. In this section,we mainly introducesome basic notations and properties which will be used in the later part of this paper.The third chapter mainly gives some equivalent of the boundedness and compact-ness of the integral type operator Cg from the B1space to Bαin the unit disk.The fourth chapter we characterizes the boundedness of the diferences of theproducts of the composition operators from the mixed-norm spaceHp,q,γto the weightedspace H∞φtype space on the unit ball ofCn.