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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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.

Article information

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

Dates
First available in Project Euclid: 1 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1149166779

Digital Object Identifier
doi:10.2969/jmsj/1149166779

Mathematical Reviews number (MathSciNet)
MR2228563

Zentralblatt MATH identifier
1102.31004

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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1149166779


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References

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