Hardy and Bergman spaces on hyperconvex domains and their composition operators

Evgeny A. Poletsky, Michael I. Stessin

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We introduce the scale of weighted Bergman spaces on hyperconvex domains in ℂn and use the Lelong-Jensen formula to prove some fundamental results about these spaces. In particular, generalizations of such classical results as the Littlewood subordination principle, the Littlewood-Paley identity and the change of variables formula are proven. Geometric properties of the introduced norms are revealed by the Nevanlinna counting function associated with a chosen exhaustion. In the last several sections we prove boundedness and compactness results for composition operators generated by holomorphic mappings of hyperconvex domains.

Original languageEnglish (US)
Pages (from-to)2153-2201
Number of pages49
JournalIndiana University Mathematics Journal
Volume57
Issue number5
DOIs
StatePublished - Dec 16 2008

Keywords

  • Composition operators
  • Pluripotential theory
  • Plurisubharmonic functions

ASJC Scopus subject areas

  • Mathematics(all)

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