### Abstract

On the setting of the half-space R^{n-1} × R_{+}, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic L^{p}-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.

Original language | English |
---|---|

Pages (from-to) | 269-287 |

Number of pages | 19 |

Journal | Integral Equations and Operator Theory |

Volume | 36 |

Issue number | 3 |

Publication status | Published - 2000 Mar 1 |

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### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis

### Cite this

*Integral Equations and Operator Theory*,

*36*(3), 269-287.

**Gleason's problem for harmonic Bergman and Bloch functions on half-spaces.** / Choe, Boo Rim; Koo, Hyung Woon; Yi, Heungsu.

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 36, no. 3, pp. 269-287.

}

TY - JOUR

T1 - Gleason's problem for harmonic Bergman and Bloch functions on half-spaces

AU - Choe, Boo Rim

AU - Koo, Hyung Woon

AU - Yi, Heungsu

PY - 2000/3/1

Y1 - 2000/3/1

N2 - On the setting of the half-space Rn-1 × R+, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic Lp-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.

AB - On the setting of the half-space Rn-1 × R+, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic Lp-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.

UR - http://www.scopus.com/inward/record.url?scp=0013275359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013275359&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0013275359

VL - 36

SP - 269

EP - 287

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

ER -