Cauchy-type integrals in several complex variables
Tóm tắt
We present the theory of Cauchy–Fantappié 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–Szegö and Bergman projection operators (which are not of Cauchy–Fantappié type).
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