Composition operators on strictly pseudoconvex domains with smooth symbol

Hyungwoon Koo, Song Ying Li

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is well known that the composition operator CΦ is unbounded on Hardy and Bergman spaces on the unit ball Bn in ℂn when n > 1 for a linear holomorphic self-map Φ of Bn. We find a sufficient and necessary condition for a composition operator with smooth symbol to be bounded on Hardy or Bergman spaces over a bounded strictly pseudoconvex domain in ℂn. Moreover, we show that this condition is equivalent to the compactness of the composition operator from a Hardy or Bergman space into the Bergman space whose weight is 1/4 bigger. We also prove that a certain jump phenomenon occurs when the composition operator is not bounded. Our results generalize known results on the unit ball to strictly pseudoconvex domains.

Original languageEnglish
Pages (from-to)135-153
Number of pages19
JournalPacific Journal of Mathematics
Volume268
Issue number1
DOIs
Publication statusPublished - 2014

Keywords

  • Boundedness
  • Composition operator
  • Smooth symbol
  • Strictly pseudoconvex domain

ASJC Scopus subject areas

  • Mathematics(all)

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