Composition Operators on Bounded Convex Domains in Cn

Hyungwoon Koo, Song Ying Li

Research output: Contribution to journalArticlepeer-review

Abstract

We study composition operators on a class of bounded domains including convex domains Ω ⊂ Cn. We show that a general self-map ϕ of Ω always induces a bounded operator Cϕ:Aαp(Ω)→Aα+n-1p(Ω) and the weight gain n- 1 is optimal in certain sense. When ϕ is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.

Original languageEnglish
Pages (from-to)555-572
Number of pages18
JournalIntegral Equations and Operator Theory
Volume85
Issue number4
DOIs
Publication statusPublished - 2016 Aug 1

Keywords

  • Boundedness
  • Composition operator
  • Convex domain
  • Finite type domain
  • Smooth symbol

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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