On the Bergman kernel for some Hartogs domains
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 521-533
https://doi.org/10.4134/BKMS.b190382
Published online March 31, 2020
Jong-Do Park
Kyung Hee University
Abstract : {In this paper, we compute the Bergman kernel for $$\Omega_{p,q,r}=\{(z,z',w)\in\ch{\mathbb{C}^2\times\Delta} : |z|^{2p}<(1-|z'|^{2q})(1-|w|^2)^r\},$$ where $p,q,r>0$ in terms of multivariable hypergeometric series. As a consequence, we obtain the \ch{behavior} of $$K_{\Omega_{p,q,r}}(z,0,0;z,0,0)$$ \ch{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
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