Singularities of the Szegِ Kernel for Certain Weakly Pseudoconvex Domains in C2

We study the Szegِ kernel for a class of weakly pseudoconvex domains in C2. Starting from an integral representation of the Szegِ, kernel on the boundary of the domain we derive a complete asymptotic expansion of the main part of the integral kernel, which gives, near boundary points of finite type, a full description of the singularities up to a bounded function. Finally we point out how one can extend the results to more general domains.