The Szegö kernel for certain non-pseudoconvex domains in C^2

Abstract

We consider the Szegö kernel for domains Ωin C^2 given by Ω= {(z,w): Im w > b(Re z)} where b is a non-convex quartic polynomial with positive leading coefficient. Such domains are not pseudoconvex. We describe the subset of \barΩ \times \barΩ on which the kernel and all its derivatives are finite. In particular, we show that there are points off the diagonal of the boundary at which the Szegö kernel is infitie as well as points on the diagonal at which it is finite.

25 pages. To appear in the Illnois J. Math