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.
Hyungwoon KOO. Kyesook NAM. Heungsu YI. "Weighted harmonic Bergman kernel on half-spaces." J. Math. Soc. Japan 58 (2) 351 - 362, April, 2006. https://doi.org/10.2969/jmsj/1149166779