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 i...

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Veröffentlicht in:Bulletin of mathematical sciences Jg. 3; H. 2; S. 241 - 285
Hauptverfasser: Lanzani, Loredana, Stein, Elias M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.08.2013
World Scientific Publishing Co. Pte., Ltd
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ISSN:1664-3607, 1664-3615
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Zusammenfassung: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).
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1664-3607
1664-3615
DOI:10.1007/s13373-013-0038-y