Characterizations for Inner Functions in Certain Function Spaces

Atte Reijonen, Toshiyuki Sugawa

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For 12<p<∞, 0 < q< ∞ and a certain two-sided doubling weight ω, we characterize those inner functions Θ for which ‖Θ′‖Aωp,qq=∫01(∫02π|Θ′(reiθ)|pdθ)q/pω(r)dr<∞.Then we show a modified version of this result for p⩾ q. Moreover, two additional characterizations for inner functions whose derivative belongs to the Bergman space Aωp,p are given.

Original languageEnglish
Pages (from-to)1853-1871
Number of pages19
JournalComplex Analysis and Operator Theory
Volume13
Issue number4
DOIs
Publication statusPublished - 2019 Jun 1

Keywords

  • Bergman space
  • Blaschke product
  • Frostman shift
  • Hardy space
  • Inner function
  • Mixed norm space

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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