Difference of weighted composition operators

Boo Rim Choe, Koeun Choi, Hyungwoon Koo, Jongho Yang

Research output: Contribution to journalArticle

Abstract

We obtain complete characterizations in terms of Carleson measures for bounded/compact differences of weighted composition operators acting on the standard weighted Bergman spaces over the unit disk. Unlike the known results, we allow the weight functions to be non-holomorphic and unbounded. As a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the Hardy spaces in terms of Carleson measures and, as a nontrivial application of this, we show that compact differences of composition operators with univalent symbols on the Hardy spaces are exactly the same as those on the weighted Bergman spaces. As another application, we show that an earlier characterization due to Acharyya and Wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of non-holomorphic weights. We also include some explicit examples related to our results.

Original languageEnglish
Article number108401
JournalJournal of Functional Analysis
Volume278
Issue number5
DOIs
Publication statusPublished - 2020 Mar 15

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Keywords

  • Bergman space
  • Difference
  • Hardy space
  • Weighted composition operator

ASJC Scopus subject areas

  • Analysis

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