Representations and interpolations of harmonic Bergman functions on half-spaces

Boo Rim Choe, Heungsu Yi

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

On the setting of the half-space of the euclidean n-space, we prove representation theorems and interpolation theorems for harmonic Bergman functions in a constructive way. We also consider the harmonic (little) Bloch spaces as limiting spaces. Our results show that well-known phenomena for holomorphic cases continue to hold. Our proofs of representation theorems also yield a uniqueness theorem for harmonic Bergman functions. As an application of interpolation theorems, we give a distance estimate to the harmonic little Bloch space. In the course of the proofs, pseudohyperbolic balls are used as substitutes for Bergman metric balls in the holomorphic case.

Original languageEnglish
Pages (from-to)51-89
Number of pages39
JournalNagoya Mathematical Journal
Volume151
DOIs
Publication statusPublished - 1998 Sep

ASJC Scopus subject areas

  • Mathematics(all)

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