THE SZEGOE KERNEL FOR CERTAIN NON-PSEUDOCONVEX DOMAINS IN C~2

摘要

We consider the Szegoe kernel for domains in C~2 given by Ω = {(z,w): Im(w) > b(Re(z))} for b a non-convex quartic polynomial with positive leading coefficient. Such domains are not pseudoconvex. We describe a subset of Ω × Ω on which the kernel and all of its derivatives are finite. We show that there are points off the diagonal of partial derivΩ × partial derivΩ at which the Szegoe kernel is infinite as well as points on the diagonal at which it is finite.