THE BERGMAN PROJECTION AS A SINGULAR INTEGRAL OPERATOR

We show that the Bergman projection operator, associated to one of three classes of domains (all smoothly bounded)-a finite type domain C2; a decoupled, finite type domain in C(n); or a convex, finite type domain in C(n)-may be viewed as a generalized Calderon-Zygmund operator. As an application of this observation, we show that the Bergman projector on any of these domains preserves the Lebesgue classes L(p), 1 < p < infinity.