Compact and Hilbert-Schmidt weighted composition operators on weighted Bergman spaces

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Abstract

Let u and be two analytic functions on the unit disk D such that. A weighted composition operator induced by u and is defined on, the weighted Bergman space of D, by for every. We obtain sufficient conditions for the compactness of in terms of function-theoretic properties of u and. We also characterize when on is Hilbert-Schmidt. In particular, the characterization is independent of when is an automorphism of D. Furthermore, we investigate the Hilbert-Schmidt difference of two weighted composition operators on.

Original languageEnglish
Pages (from-to)208-225
JournalJournal of the Australian Mathematical Society
Volume113
Issue number2
DOIs
Publication statusPublished - Oct 2022

Keywords

  • 47B33 30H20

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