Bergman kernel for some generalized Hartogs domains
Bull. Korean Math. Soc.
Published online October 17, 2019
Jong-Do Park
Kyung Hee University
Abstract : In this paper, we compute the Bergman kernel for
$$\Omega_{p,q,r}=\{(z,z',w)\in\mathbb{C}^3 : |z|^{2p}<(1-|z'|^{2q})(1-|w|^2)^r\},$$
where $p,q,r>0$ in terms of multivariable hypergeometric series.
As a consequence, we obtain the boundary behavior of
$$K_{\Omega_{p,q,r}}(z,0,0;z,0,0)$$ on the diagonal when $(z,0,0)$ approaches to the boundary of $\Omega_{p,q,r}$.
Keywords : Bergman kernel, Hartogs domain, hypergeometric series
MSC numbers : 32A25, 32A07, 33C05
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