Representations and interpolations of harmonic Bergman functions on half-spaces

Abstract

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.