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.; Stein E.M.. - In: BULLETIN OF MATHEMATICAL SCIENCES. - ISSN 1664-3607. - ELETTRONICO. - 3:2(2013), pp. 241-285. [10.1007/s13373-013-0038-y]
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
