Composition operators on holomorphic Sobolev spaces in Bn

Hyung Woon Koo, Inyoung Park

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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,s p, and prove the jump phenomenon of CΦ on Aα,s p. Moreover, we show an interesting result that the boundedness of CΦ on Aα,s p is equivalent to the compactness of CΦ:Aα,s p→Aβ,t q for appropriate Aβ,t q, for example Aβ,t q=Aα+1/4,s p. 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
Volume369
Issue number1
DOIs
Publication statusPublished - 2010 Sep 1

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Sobolev spaces
Composition Operator
Sobolev Spaces
Compactness
Mathematical operators
Boundedness
Chemical analysis
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Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Composition operators on holomorphic Sobolev spaces in Bn . / Koo, Hyung Woon; Park, Inyoung.

In: Journal of Mathematical Analysis and Applications, Vol. 369, No. 1, 01.09.2010, p. 232-244.

Research output: Contribution to journalArticle

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