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 Ω ⊂ C² under the assumption that bΩ 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 Ω is exactly regular on the non-isotropic Sobolev spaces NL^p_k(bΩ) for 1 < p < +∞ and k = 0, 1, ., and also that S: Γα(E) → Γα(bΩ), for E bΩ and 0 < α < +∞, with a bound that depends only on diam(E), where Γα are the non-isotropic Hölder spaces.