Compact double differences of composition operators on the Bergman spaces over the ball

Research output: Contribution to journalArticle

Abstract

Choe et al. have recently characterized compact double differences formed by four composition operators acting on the standard weighted Bergman spaces over the disk of the complex plane. In this paper, we extend such a result to the ball setting. Our characterization is obtained under a suitable restriction on inducing maps, which is automatically satisfied in the case of the disk. We exhibit concrete examples, for the first time even for single composition operators, which shows that such a restriction is essential in the case of the ball.

Original languageEnglish
Pages (from-to)609-637
Number of pages29
JournalTohoku Mathematical Journal
Volume71
Issue number4
DOIs
Publication statusPublished - 2019 Dec

Keywords

  • Ball
  • Compact operator
  • Composition operator
  • Double difference
  • Weighted Bergman space

ASJC Scopus subject areas

  • Mathematics(all)

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