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
File Format
Degree Grantor
University of Nevada, Las Vegas
Language
English
Repository Citation
Huo, Ming, "Weighted Composition Operators on a Bergman-type Reproducing Kernel Hilbert Space" (2019). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3727.
http://dx.doi.org/10.34917/16076267
Rights
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