Composition operators on strictly pseudoconvex domains with smooth symbol

Hyung Woon Koo, Song Ying Li

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is well known that the composition operator CΦ is unbounded on Hardy and Bergman spaces on the unit ball Bn in ℂn when n > 1 for a linear holomorphic self-map Φ of Bn. We find a sufficient and necessary condition for a composition operator with smooth symbol to be bounded on Hardy or Bergman spaces over a bounded strictly pseudoconvex domain in ℂn. Moreover, we show that this condition is equivalent to the compactness of the composition operator from a Hardy or Bergman space into the Bergman space whose weight is 1/4 bigger. We also prove that a certain jump phenomenon occurs when the composition operator is not bounded. Our results generalize known results on the unit ball to strictly pseudoconvex domains.

Original languageEnglish
Pages (from-to)135-153
Number of pages19
JournalPacific Journal of Mathematics
Volume268
Issue number1
DOIs
Publication statusPublished - 2014 Jan 1

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Pseudoconvex Domain
Bergman Space
Composition Operator
Strictly
Hardy Space
Unit ball
Compactness
Jump
Necessary Conditions
Generalise
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Composition operators on strictly pseudoconvex domains with smooth symbol. / Koo, Hyung Woon; Li, Song Ying.

In: Pacific Journal of Mathematics, Vol. 268, No. 1, 01.01.2014, p. 135-153.

Research output: Contribution to journalArticle

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