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Representations and interpolations of harmonic Bergman functions on half-spaces

Published online by Cambridge University Press:  22 January 2016

Boo Rim Choe  and
Heungsu Yi
Boo Rim Choe
Affiliation:
Department of Mathematics, Korea University, Seoul 136-701, Korea, choebr@semi.korea.ac.kr
Heungsu Yi
Affiliation:
Department of Mathematics, Research Institute of Basic Sciences, Kwangwoon University, Seoul 139-701, Korea, hsyi@euler.kwangwoon.ac.kr
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Abstract.

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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 151 , September 1998 , pp. 51 - 89
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

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