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 $z\in D$. 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).

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