Composition operators on holomorphic Sobolev spaces in Bn

Hyungwoon Koo, Inyoung Park

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We study the composition operator CΦ on holomorphic Sobolev spaces induced by an analytic self-map Φ of Bn in Cn that extends to be smooth on Bn. We characterize the boundedness and the compactness of CΦ on Aα,sp, and prove the jump phenomenon of CΦ on Aα,sp. Moreover, we show an interesting result that the boundedness of CΦ on Aα,sp is equivalent to the compactness of CΦ:Aα,sp→Aβ,tq for appropriate Aβ,tq, for example Aβ,tq=Aα+1/4,sp. We provide examples to show that our results are sharp.

Original languageEnglish
Pages (from-to)232-244
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2010 Sept

Bibliographical note

Funding Information:
✩ This work is partially supported by Korea Research Foundation Grant (KRF-2008-314-C00012).


  • Boundedness
  • Compactness
  • Composition operator
  • Holomorphic Sobolev space
  • Unit ball

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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