Some Analytic Function Spaces And The Related Weighted Composition Operators

In this paper, we mainly discuss the boundedness and compactness of the weighted composition operator on Zygmund space and little Zygmund space. We also give the Lipschitz type characterization of logarithmic Bloch-type space on the open unit disk by Riemannian distance. At the same time we discuss the bounded-ness of the weighted composition operator from Hardy space to Growth-type space, Bloch space and Zygmund space over the upper half-plane. There are four chapters in the paper.In Chapter1, we mainly introduce some definitions of analytic function spaces and operators. We also list some results to the thesis.In Chapter2, we concern study the boundedness and compactness of the weight-ed composition operator on Zygmund space and little Zygmund space on the open unit disk, and then we get some sufficient and necessary conditions for boundedness of these weighted composition operators.In Chapter3, we define a Riemannian distance and then we give the Lipschitz type characterization of logarithmic Bloch-type space on the open unit disk.In Chapter4, we devoted to investigatethe the boundedness of the weighted composition operator H∞Hardy space to Growth-type space, Bloch space and Zygmund space over the upper half-plane. Some sufficient and necessary conditions are given for boundedness of these weighted composition operators.