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

Hyungwoon Koo, Wayne Smith

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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 : Aαp (BN) → Aα + 1 / 4 - ε{lunate}p (BN), then CΨ is bounded on Aαp (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
Issue number1
Publication statusPublished - 2007 May 1


  • Bergman space
  • Composition operator
  • Unit ball

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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