Award Date

December 2022

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

First Committee Member

Zhijian Wu

Second Committee Member

Xin Li

Third Committee Member

Angel Muleshkov

Fourth Committee Member

Stephen Lepp


Our focus is differences of weighted composition operators on Hardy and Bergman spaces. Earl Berkson first motivated studying differences of composition operators in 1981. Since then many authors have dug into analyzing the properties of these operators on Hardy and Bergman spaces. For example, we already know that such operators are bounded on these spaces, but they are not always compact. Authors have done much investigation into when these differences are compact. Authors have also investigated when these differences are Hilbert-Schmidt. These results rely on conditions to be met by both of the composition operators involved in the difference. Our contribution here is to show results about compactness and Hilbert-Schmidt of these weighted differences involving only one of the weighted composition operators. We also investigate conditions under which they may belong to the Schatten p-class of operators, for p= 4, again only involving one of the weighted composition operators instead of both.



Degree Grantor

University of Nevada, Las Vegas




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