Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE BERGMAN KERNEL FOR SOME HARTOGS DOMAINS

  • Park, Jong-Do (Department of Mathematics and Research Institute for Basic Sciences Kyung Hee University)
  • Received : 2019.04.10
  • Accepted : 2019.08.05
  • Published : 2020.03.31

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.

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Acknowledgement

Supported by : National Research Foundation of Korea

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