### Abstract

On the setting of the upper half-space H of the Euclidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < ∞ and nonorthogonal projections for 1 ≤ p < ∞. Using these results, we show that Bergman norm is equivalent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b_{α}^{1}.

Original language | English |
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Pages (from-to) | 975-1002 |

Number of pages | 28 |

Journal | Journal of the Korean Mathematical Society |

Volume | 42 |

Issue number | 5 |

Publication status | Published - 2005 Sep 1 |

### Fingerprint

### Keywords

- Fractional derivative
- Harmonic Bergman functions
- Upper half-space
- Weighted Bergman kernel

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Korean Mathematical Society*,

*42*(5), 975-1002.

**Weighted harmonic bergman functions on half-spaces.** / Koo, Hyung Woon; Nam, Kyesook; Heungsu, Y. I.

Research output: Contribution to journal › Article

*Journal of the Korean Mathematical Society*, vol. 42, no. 5, pp. 975-1002.

}

TY - JOUR

T1 - Weighted harmonic bergman functions on half-spaces

AU - Koo, Hyung Woon

AU - Nam, Kyesook

AU - Heungsu, Y. I.

PY - 2005/9/1

Y1 - 2005/9/1

N2 - On the setting of the upper half-space H of the Euclidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < ∞ and nonorthogonal projections for 1 ≤ p < ∞. Using these results, we show that Bergman norm is equivalent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of bα1.

AB - On the setting of the upper half-space H of the Euclidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < ∞ and nonorthogonal projections for 1 ≤ p < ∞. Using these results, we show that Bergman norm is equivalent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of bα1.

KW - Fractional derivative

KW - Harmonic Bergman functions

KW - Upper half-space

KW - Weighted Bergman kernel

UR - http://www.scopus.com/inward/record.url?scp=25444469921&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25444469921&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:25444469921

VL - 42

SP - 975

EP - 1002

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

SN - 0304-9914

IS - 5

ER -