### 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 |
---|---|

Pages (from-to) | 51-89 |

Number of pages | 39 |

Journal | Nagoya Mathematical Journal |

Volume | 151 |

Publication status | Published - 1998 Sep 1 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Nagoya Mathematical Journal*,

*151*, 51-89.

**Representations and interpolations of harmonic Bergman functions on half-spaces.** / Choe, Boo Rim; Yi, Heungsu.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Representations and interpolations of harmonic Bergman functions on half-spaces

AU - Choe, Boo Rim

AU - Yi, Heungsu

PY - 1998/9/1

Y1 - 1998/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0013316568&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013316568&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0013316568

VL - 151

SP - 51

EP - 89

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -