On the Bergman kernel for some Hartogs domains
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 521-533
Published online October 17, 2019
Printed March 31, 2020
Jong-Do Park
Kyung Hee University
Abstract : {In this paper, we compute the Bergman kernel for
$$\Omega_{p,q,r}=\{(z,z',w)\in\{{\mathbb{C}^2\times\Delta} : |z|^{2p}<(1-|z'|^{2q})(1-|w|^2)^r\},$$
where $p,q,r>0$ in terms of multivariable hypergeometric series.
As a consequence, we obtain the behavior of
$$K_{\Omega_{p,q,r}}(z,0,0;z,0,0)$$ when $(z,0,0)$ approaches} to the boundary of $\Omega_{p,q,r}$.
Keywords : Bergman kernel, Hartogs domain, hypergeometric series
MSC numbers : Primary 32A25, 32A07, 33C05
Supported by : This work was supported by NRF-2018R1D1A1B07050044 from National Research Foundation of Korea.
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