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On the Bergman kernel for some Hartogs domains

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대한수학회 (The Korean Mathematical Society)|2020.03|대한수학회보 (Bulletin of the KMS)|제57권 제2호|pp. 521-533|DOI 10.4134/BKMS.b190382

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키워드

hypergeometric seriesBergman kernelHartogs domain
주제분류수학

초록

{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 $\Omega_{p,q,r}$. }

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 $\Omega_{p,q,r}$. }

참고문헌 (18)

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