Award Date

8-1-2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Zhijian Wu

Second Committee Member

Angel Muleshkov

Third Committee Member

Monika Neda

Fourth Committee Member

Stephen Lepp

Number of Pages

81

Abstract

In this research, we introduce a Bergman-type reproducing kernel Hilbert space A2 ρ and consider the weighted composition operators uCφ acting on A2 ρ . We first investigate the properties of A2 ρ and make assumptions in terms of its weight ρ and reproducing kernel functions Kz. Based on the assumptions and the use of Carleson measures, characterizations are established for uCφ the weighted composition operators being bounded or compact on A2 ρ , which shows that the reproducing kernel function plays a meaningful role in the characterization of uCφ. We also characterize the compactness of uCφ − vCψ on A2 ρ , which involves some kind of non-Euclidean distance between φ and ψ, which is called pseudohyperbolic distance, and the reproducing kernel function of A2 ρ . Finally, we give an explicit formula of the Hilbert Schmidt norm of uCφ − vCψ. Especially, our results coincide with the corresponding results in Bergman space (A2 ρ = A2 α ).

Keywords

Bergman Space; Composition Operator

Disciplines

Mathematics

Language

English

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