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Winter 2007 Estimates for the Szegö kernel on a model non-pseudoconvex domain
Christine Carracino
Illinois J. Math. 51(4): 1363-1396 (Winter 2007). DOI: 10.1215/ijm/1258138550

Abstract

The Szegö kernel $S(z,\zeta)$ on the boundary of strictly pseudoconvex domains has been studied extensively. We can consider model domains $\Omega = \{ (z_1,z_2) \in \mathbb{C}^2 \mid -\Im z_2 > b(\Re z_1)\}$. If $b$ is convex, one has $|S(z,\zeta)| \le c|B(z,\delta)|^{-1}$, where $B(z,\delta)$ is the nonisotropic ball with center $z$ and radius $\delta$, and $\delta $ is the nonisotropic distance from $z$ to $\zeta$. The only singularities are on the diagonal $z=\zeta$. In this paper, we obtain estimates for $|S|$ when the function $b$ is a certain non-convex function. We show that near certain points, there are singularities off the diagonal.

Citation

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Christine Carracino. "Estimates for the Szegö kernel on a model non-pseudoconvex domain." Illinois J. Math. 51 (4) 1363 - 1396, Winter 2007. https://doi.org/10.1215/ijm/1258138550

Information

Published: Winter 2007
First available in Project Euclid: 13 November 2009

zbMATH: 1147.32003
MathSciNet: MR2417433
Digital Object Identifier: 10.1215/ijm/1258138550

Subjects:
Primary: 32A25

Rights: Copyright © 2007 University of Illinois at Urbana-Champaign

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Vol.51 • No. 4 • Winter 2007
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