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Addendum to “On the Bergman kernel of hyperconvex domains”, Nagoya Math. J. 129 (1993), 43–52

Published online by Cambridge University Press:  22 January 2016

Takeo Ohsawa
Takeo Ohsawa*
Affiliation:
Department of Mathematics, Nagoya University, Nagoya, 464-01, Japan
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0. In [0-1] it was proved that for any bounded hyperconvex domain D in C2 the Bergman kernel function K(z, w) of D satisfies

In case n ═ 1, this is due to a behavior of sublevel sets of the Green function. The general case then follows by the extendability of L2 holomorphic functions.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 137 , March 1995 , pp. 145 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

[0–1] Ohsawa, T., On the Bergman kernel of hyperconvex domains, Nagoya Math. J., 129 (1993), 43–52.Google Scholar
[0–2] Ohsawa, T., On the extension of L holomorphic functions III: negligible weights, to appear in Math. Z.Google Scholar
[S] Suita, N., Capacities and kernels on Riemann surfaces, Arch. Rational Mech. Anal., 46(1972), 212–217.Google Scholar