Estimates for the Szego projection on uniformly finite-type subdomains of C2

We prove precise growth and cancellation estimates for the Szego kernel of an unbounded model domain Omega subset of C-2 under the assumption that b Omega satisfies a uniform finite-type hypothesis. Such domains have smooth boundaries which are not algebraic varieties, and therefore admit no global homogeneities that allow one to use compactness arguments in order to obtain results. As an application of our estimates, we prove that the Szego projection S of Omega is exactly regular on the non-isotropic Sobolev spaces NLkp (b Omega) for 1 < p < +infinity and k = 0, 1, . . . , and also that S: Gamma(alpha)(E) -> Gamma(alpha)(b Omega), for E is an element of b Omega and 0 < alpha < +infinity, with a bound that depends only on diam(E), where Gamma(alpha) are the non-isotropic Holder spaces.