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 Lp estimates for these operators and, as a consequence, to obtain Lp estimates for the canonical Cauchy–Szegö and Bergman projection operators (which are not of Cauchy–Fantappié type).

Cauchy-type integrals in several complex variables

Lanzani L.
;
2013

Abstract

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 Lp estimates for these operators and, as a consequence, to obtain Lp estimates for the canonical Cauchy–Szegö and Bergman projection operators (which are not of Cauchy–Fantappié type).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/873306
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