Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 58, Number 2 (2006), 351-362.
Weighted harmonic Bergman kernel on half-spaces
Hyungwoon KOO, Kyesook NAM, and Heungsu YI
Abstract
On the setting of the upper half-space of the Euclidean -space, we study weighted harmonic Bergman functions as follows. First, we define the fractional derivatives of some functions defined on . 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