Three Projection Operators in Several Complex Variables

I will report on recent joint work with L. Lanzani on three basic projection operators, each associated to an appropriate domain in C^n. These are: variants of Cauchy-Fantappie integrals; the Cauchy-Szego projection: and the Bergman projection. The results obtained give L^p boundedness of these oprators under minimal smoothness assumptions of the boundary of the domain.