Journal of Lie Theory 21 (2011), No. 4, 755--769
Copyright Heldermann Verlag 2011
Some Estimates of the Bergman Kernel of Minimal Bounded Homogeneous Domains
Hideyuki Ishi
Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
hideyuki@math.nagoya-u.ac.jp
Satoshi Yamaji
Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
satoshi.yamaji@math.nagoya-u.ac.jp
We describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the homogeneous domain.
Keywords: Bounded homogeneous domain, Bergman kernel, minimal domain, Siegel domain.
MSC: 32A25, 32H02, 32M10
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