The Generalized Weighted Composition Operators Between Bloch-type Spaces In The Unit Disk

In this thesis, we mainly investigate some properties of the generalized weighted composition operators μCφDm between Bloch-type spaces and Zygmund-type spaces in the unit disk, including the boundedness, compactness and the estimations of essential norm.The content of this thesis is divided into three chapters.The first chapter is about the introduction. Some basic conceptions related to the research of the content of this paper are given, and some main results of the research are presented. Additionally, the background of the research, the history of its development and the current situation of the boundedness, compactness and essential norms of the composition operator, weighted composition operators on the correlation function space are described.The second chapter discusses the essential norms of the μCφDm:Bαâ†'Bβ , and through the using of the integral operator Iμ and Jμ, an equivalent characterization for essential norm of the μCφDm is given. The μCφDm:Bαâ†'Bβ are consequently derived as the sufficient and necessary condition of the compact operator.The third chapter discusses the boundedness of the μCφDm between Zygmund-type spaces in the unit disk. Based on spatial equivalent characteristics of Zygmund-type spaces Zα, and combined with the qualitative analysis of the μ and φ, as well as through the discussion of a and m, the sufficient and necessary conditions for boundedness of the μCφDm:Zαâ†'Zβ are given respectively.