Generalized Weighted Composition Operators on Analytic Function Spaces

The study of composition operators and weighted composition operators lies at the interface of operator theory and function theory. Composition operators and weighted composition operators occur naturally in a variety of problems. Moreover, they are closely related to many famous problems, such as invariant subspace problem, Bieberbach's conjecture and Brennan's conjecture. This book is a collection of my recent published papers in area of "Generalized weighted composition operators on analytic function spaces". The book consists of five chapters, organized as follows. In chapter 1, we briefly recall the history of composition operators and weighted composition operators on some function spaces in the unit disk. In Chapter 2 we introduce some concepts used in this book. In Chapter 3 we study generalized weighted composition operators on Bloch type spaces. The differences of generalized weighted composition operators on Bloch type spaces are also investigated. In Chapter 4 we study generalized weighted composition operators on weighted Bergman spaces. In Chapter 5 we present some topics which require further research.