Doctor of Philosophy (PhD)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
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 ).
Bergman Space; Composition Operator
Huo, Ming, "Weighted Composition Operators on a Bergman-type Reproducing Kernel Hilbert Space" (2019). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3727.
Available for download on Wednesday, May 15, 2024