Weighted Composition Operators On The Bloch-type And Weighted Bergman Spaces In The Polydisc

This dissertation investigates the weighted composition operators ψCφ on the Bloch-type and weighted Bergman spaces in the unit polydisc. We obtain the nature of weighted composition operators on the two holomorphic function spaces,by applying the definitions of weighted composition operators and the function spaces, and the related nature of essential norms, futhermore selecting the appropriate test functions.This thesis consists of three chapters:The first chapter is the introduction. It mainly discusses the research back-ground, research situation and research significance of the problem, giving the basic definitions and symbols.The second chapter investigates the essential norms of the weighted compo-sition operator ψCφ between Bloch-type spaces in the unit polydisc, and gives the lower and upper estimates of the essential norms, by estimating the value of the functions of Bloch-type spaces and selecting the appropriate test functions.The third chapter describes the sufficient and necessary conditions for the weighted composition operator ψCφ to be bounded and compact from weighted Bergman space to the Bloch-type spaces, in terms of the function properties of φ and φ. And gives the estimate of the essential norm by applying the bounded conditions.