### Abstract

On the setting of the upper half-space H of the Euclidean n-space, we study weighted harmonic Bergman functions as follows. First, we define the fractional derivatives of some functions defined on H. Next, we find the explicit formula for weighted Bergman kernel through the fractional derivative of the extended Poisson kernel and then we give the size estimates for derivatives of this kernel.

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

Pages (from-to) | 351-362 |

Number of pages | 12 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 58 |

Issue number | 2 |

Publication status | Published - 2006 Apr 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 Mathematical Society of Japan*,

*58*(2), 351-362.

**Weighted harmonic Bergman kernel on half-spaces.** / Koo, Hyung Woon; Nam, Kyesook; Yi, Heungsu.

Research output: Contribution to journal › Article

*Journal of the Mathematical Society of Japan*, vol. 58, no. 2, pp. 351-362.

}

TY - JOUR

T1 - Weighted harmonic Bergman kernel on half-spaces

AU - Koo, Hyung Woon

AU - Nam, Kyesook

AU - Yi, Heungsu

PY - 2006/4/1

Y1 - 2006/4/1

N2 - On the setting of the upper half-space H of the Euclidean n-space, we study weighted harmonic Bergman functions as follows. First, we define the fractional derivatives of some functions defined on H. Next, we find the explicit formula for weighted Bergman kernel through the fractional derivative of the extended Poisson kernel and then we give the size estimates for derivatives of this kernel.

AB - On the setting of the upper half-space H of the Euclidean n-space, we study weighted harmonic Bergman functions as follows. First, we define the fractional derivatives of some functions defined on H. Next, we find the explicit formula for weighted Bergman kernel through the fractional derivative of the extended Poisson kernel and then we give the size estimates for derivatives of this kernel.

KW - Fractional derivative

KW - Harmonic Bergman functions

KW - Upper half-space

KW - Weighted Bergman kernel

UR - http://www.scopus.com/inward/record.url?scp=33745615841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745615841&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33745615841

VL - 58

SP - 351

EP - 362

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -