On the Bergman kernel in weighted monogenic Bargmann-Fock spaces

Abstract

In this paper, we study the Bergman kernel $B_\varphi(x,y)$ of generalized Bargmann-Fock spaces in the setting of Clifford algebra. The versions of $L^2$-estimate method and weighted subharmonic inequality for Clifford algebra are established. Consequently we show the existence of $B_\varphi(x,y)$ and then give some estimates on and off the diagonal. As a by-product, we also obtain an upper estimate of the weighted harmonic Bergman kernel.