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http://dx.doi.org/10.4134/BKMS.b190382

ON THE BERGMAN KERNEL FOR SOME HARTOGS DOMAINS  

Park, Jong-Do (Department of Mathematics and Research Institute for Basic Sciences Kyung Hee University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 521-533 More about this Journal
Abstract
In this paper, we compute the Bergman kernel for Ωp,q,r = {(z, z', w) ∈ ℂ2 × Δ : |z|2p < (1 - |z'|2q)(1 - |w|2)r}, 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.
Keywords
Bergman kernel; Hartogs domain; hypergeometric series;
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