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Cauchy-type integrals in several complex variables
We present the theory of Cauchy-Fantappi\'e integral operators, with emphasis
on the situation when the domain of integration, , 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 . The goal is to prove
estimates for these operators and, as a consequence, to obtain estimates
for the canonical Cauchy-Szeg\"o and Bergman projection operators (which are
not of Cauchy-Fantappi\'e type).Comment: This is an electronic reprint of the original article published in
the Bulletin of the Mathematical Sciences, vol. 3 (2) (2013) 241-285. This
reprint differs from the original in pagination and typographical detai
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