Derivatives of Harmonic Bergman and Bloch Functions on the Ball

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24 Citations (Scopus)

Abstract

On the setting of the unit ball of euclidean n-space, we investigate properties of derivatives of functions in the harmonic Bergman space and the harmonic Bloch space. Our results are (1) size estimates of derivatives of the harmonic Bergman kernel, (2) Gleason's problem, and (3) characterizations in terms of radial, tangential, and ordinary derivative norms. In the course of proofs, some reproducing formulas are found and estimated.

Original languageEnglish
Pages (from-to)100-123
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Volume260
Issue number1
DOIs
Publication statusPublished - 2001 Aug 1

Keywords

  • Harmonic Bergman and Bloch functions; Gleason's problem; derivative norms

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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