Composition operators induced by smooth self-maps of the unit ball in CN

Hyung Woon Koo, Wayne Smith

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We study the composition operator CΨ induced by an analytic self-map Ψ of the unit ball BN in CN that extends to be smooth on over(B, -)N. When Ψ is of class C3 on over(B, -)N, we extend to weighted Bergman spaces W.R. Wogen's characterization of when CΨ is bounded on Hp (BN). Next, when Ψ is of class C4 on over(B, -)N, we show that if ε{lunate} > 0 and CΨ : Aα p (BN) → Aα + 1 / 4 - ε{lunate} p (BN), then CΨ is bounded on Aα p (BN). The discrete jump of size 1/4 in the exponent of the weight is sharp. Examples are given that show the assumption Ψ is smooth is essential in these theorems.

Original languageEnglish
Pages (from-to)617-633
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume329
Issue number1
DOIs
Publication statusPublished - 2007 May 1

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Keywords

  • Bergman space
  • Composition operator
  • Unit ball

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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