Journal of the Mathematical Society of Japan

Weighted harmonic Bergman kernel on half-spaces

Hyungwoon KOO, Kyesook NAM, and Heungsu YI

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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.

Article information

J. Math. Soc. Japan, Volume 58, Number 2 (2006), 351-362.

First available in Project Euclid: 1 June 2006

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Zentralblatt MATH identifier

Primary: 31B05: Harmonic, subharmonic, superharmonic functions
Secondary: 31B10: Integral representations, integral operators, integral equations methods 30D45: Bloch functions, normal functions, normal families 30D55

weighted Bergman kernel harmonic Bergman functions fractional derivative upper half-space


KOO, Hyungwoon; NAM, Kyesook; YI, Heungsu. Weighted harmonic Bergman kernel on half-spaces. J. Math. Soc. Japan 58 (2006), no. 2, 351--362. doi:10.2969/jmsj/1149166779.

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