Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants

Andreas Hartmann, Xavier Massaneda, Artur Nicolau, Pascal Thomas

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)

Abstract

We consider a free interpolation problem in Nevanlinna and Smirnov classes and find a characterization of the corresponding interpolating sequences in terms of the existence of harmonic majorants of certain functions. We also consider the related problem of characterizing positive functions in the disk having a harmonic majorant. An answer is given in terms of a dual relation which involves positive measures in the disk with bounded Poisson balayage. We deduce necessary and sufficient geometric conditions, both expressed in terms of certain maximal functions. © 2004 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)1-37
JournalJournal of Functional Analysis
Volume217
Issue number1
DOIs
Publication statusPublished - 1 Dec 2004

Keywords

  • Free interpolation
  • Harmonic majorants
  • Poisson balayage
  • Smirnov and Nevanlinna class

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