### 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 language | English |
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Pages (from-to) | 51-89 |

Number of pages | 39 |

Journal | Nagoya Mathematical Journal |

Volume | 151 |

Publication status | Published - 1998 Sep 1 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Choe, B. R., & Yi, H. (1998). Representations and interpolations of harmonic Bergman functions on half-spaces.

*Nagoya Mathematical Journal*,*151*, 51-89.