Composition operators induced by smooth self-maps of the real or complex unit balls

Hyungwoon Koo, Maofa Wang

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

In this paper, we study the composition operator CΦ with a smooth but not necessarily holomorphic symbol Φ. A necessary and sufficient condition on Φ for CΦ to be bounded on holomorphic (respectively harmonic) weighted Bergman spaces of the unit ball in Cn (respectively Rn) is given. The condition is a real version of Wogen's condition for the holomorphic spaces, and a non-vanishing boundary Jacobian condition for the harmonic spaces. We also show certain jump phenomena on the weights for the target spaces for both the holomorphic and harmonic spaces.

Original languageEnglish
Pages (from-to)2747-2767
Number of pages21
JournalJournal of Functional Analysis
Volume256
Issue number9
DOIs
Publication statusPublished - 2009 May 1

Bibliographical note

Funding Information:
✩ Koo is partially supported by the KRF-2008-314-C00012 and Wang is partially supported by the NSF-10671147 and NSF-10571044 of China. * Corresponding author. E-mail addresses: koohw@korea.ac.kr (H. Koo), mfwang.math@whu.edu.cn (M. Wang).

Keywords

  • Bergman space
  • Boundedness
  • Carleson measure
  • Composition operator
  • Smooth map
  • Unit ball

ASJC Scopus subject areas

  • Analysis

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