Weighted Composition Operators And Extended Cesàro Operators On Certain Holomorphic Function Spaces

The researches of the operator theory of holomorphic function spaces have profound theoretical significance and wide application background. This paper we study the weighted composition operators and extended Cesaro operator between holomorphic function spaces. The main work of this paper is as follows:1, Introduce the main work of this paper and the main content.2, Introduce some important concept and theory of holomorphic function spaces.3, First introduce some basic properties of Bloch space, and give two useful comments. Then we prove sufficient and necessary conditions for weighted composition operators from a-Zygmund spaces into β-Bloch spaces in the unit disk to be bounded when 0< α,β< ∞.4, In this chapter, we reprove the weak convergence lemma with a brand new method, then on this basis, as well as the result of chapter 3, we prove sufficient and necessary conditions for weighted composition operators from a-Zygmund spaces into P-Bloch spaces in the unit disk to be compact when 0< α,β<∞.5, In this chapter, we prove sufficient and necessary conditions for weighted composition operators from Qk spaces into a-Bloch spaces in the unit disk to be bounded and compact when 0< α<∞.