Analytic Function Spaces And Operator Theory

In this paper, we mainly study the weighted composition operator and generalized composition operator between some spaces of analytic function on the unit disk D of the complex plane and investigate some basic properties of the analytic function space QT,s and the meromorphic function space QT,s#. The paper is divited into five chapters.Chapter 1. We first introduce the the mainly work in this paper;Chapter 2. We formulate some notations and concepts about operators and analytic function spaces;Chapter 3. We study the boundedness and compactness of the weighted composition operator from Zygmund space to weighted Bloch space and weighted Bergman space to weighted Bloch space, and give the necessary and sufficient condition.Chapter 4. We study the boundedness and compactness of the generalized composition operator from BMOA space to weighted Bloch space and weighted Bloch space. to weighted BMOA space, and give the necessary and sufficient condition.Chapter 5. We investigate some basic properties of a analytic function space QT,s and the meromorphic function space QT,s#.