Projections for harmonic Bergman spaces and applications

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Abstract

On the setting of general bounded smooth domains in Rn, we construct L1-bounded nonorthogonal projections and obtain related reproducing formulas for the harmonic Bergman spaces. In addition, we show that those projections satisfy Sobolev Lp -estimates of any order even for p=1. Among applications are Gleason's problems for the harmonic Bergman-Sobolev and (little) Bloch functions on star-shaped domains with strong reference points.

Original languageEnglish
Pages (from-to)388-421
Number of pages34
JournalJournal of Functional Analysis
Volume216
Issue number2
DOIs
Publication statusPublished - 2004 Nov 15

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Keywords

  • Gleason's problem
  • Harmonic Bergman function
  • Projection

ASJC Scopus subject areas

  • Analysis

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