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

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Composition operators on holomorphic Sobolev spaces in B<sub>n</sub>'. Together they form a unique fingerprint.

  • Cite this