Estimates of the Bergman kernel function on pseudoconvex domains with comparable Levi form

Sanghyun Cho

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J. Korean Math. Soc. 2002; 39(3): 425-437

Printed May 1, 2002

Estimates of the Bergman kernel function on pseudoconvex domains with comparable Levi form

Sanghyun Cho

Sogang University

Abstract

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Abstract

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $\mathbb C^n$ and let $z^0\in b\Omega$ be a point of finite type. We also assume that the Levi form of $b\Omega$ is comparable in a neighborhood of $z^0$. Then we get precise estimates of the Bergman kernel function, $K_\Omega(z,w)$, and its derivatives in a neighborhood of $z^0$.

Keywords: Bergman kernel function, finite type

MSC numbers: 32A25