Cauchy-type integrals in several complex variables

We present the theory of Cauchy–Fantappié integral operators, with emphasis on the situation when the domain of integration, D, has minimal boundary regularity. Among these operators we focus on those that are more closely related to the classical Cauchy integral for a planar domain, whose kernel is a holomorphic function of the parameter z ∈ D. The goal is to prove L^p estimates for these operators and, as a consequence, to obtain L^p estimates for the canonical Cauchy–Szegö and Bergman projection operators (which are not of Cauchy–Fantappié type).