Gleason's problem for harmonic Bergman and Bloch functions on half-spaces

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Abstract

On the setting of the half-space Rn-1 × R+, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic Lp-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.

Original languageEnglish
Pages (from-to)269-287
Number of pages19
JournalIntegral Equations and Operator Theory
Volume36
Issue number3
DOIs
Publication statusPublished - 2000 Mar

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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