## Illinois Journal of Mathematics

### Estimates for the Szegö kernel on a model non-pseudoconvex domain

Christine Carracino

#### 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.

#### Article information

Source
Illinois J. Math., Volume 51, Number 4 (2007), 1363-1396.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138550

Digital Object Identifier
doi:10.1215/ijm/1258138550

Mathematical Reviews number (MathSciNet)
MR2417433

Zentralblatt MATH identifier
1147.32003

#### Citation

Carracino, Christine. Estimates for the Szegö kernel on a model non-pseudoconvex domain. Illinois J. Math. 51 (2007), no. 4, 1363--1396. doi:10.1215/ijm/1258138550. https://projecteuclid.org/euclid.ijm/1258138550