Weighted harmonic Bergman kernel on half-spaces

Abstract

On the setting of the upper half-space $\mathbf{H}$ of the Euclidean $n$-space, we study weighted harmonic Bergman functions as follows. First, we define the fractional derivatives of some functions defined on $\mathbf{H}$. 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.