ON THE BERGMAN KERNEL FOR SOME HARTOGS DOMAINS

Abstract

In this paper, we compute the Bergman kernel for Ωp,q,r = {(z, z′, w) ∈ C ×∆ : |z| < (1− |z′|2q)(1− |w|)}, where p, q, r > 0 in terms of multivariable hypergeometric series. As a consequence, we obtain the behavior of KΩp,q,r (z, 0, 0; z, 0, 0) when (z, 0, 0) approaches to the boundary of Ωp,q,r.