### 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 |
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Pages (from-to) | 351-362 |

Number of pages | 12 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 58 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Koo, H., Nam, K., & Yi, H. (2006). Weighted harmonic Bergman kernel on half-spaces.

*Journal of the Mathematical Society of Japan*,*58*(2), 351-362. https://doi.org/10.2969/jmsj/1149166779