The Cauchy integral in Cn for domains with minimal smoothness

Loredana Lanzani; Elias M. Stein

doi:10.1016/j.aim.2014.07.016

The Cauchy integral in Cⁿ for domains with minimal smoothness

Loredana Lanzani, Elias M. Stein

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We prove L^p(bD)-regularity of the Cauchy-Leray integral for bounded domains D C Cⁿ whose boundary satisfies the minimal regularity condition of class C^1,1, together with a naturally occurring notion of convexity.

Original language	English (US)
Pages (from-to)	776-830
Number of pages	55
Journal	Advances in Mathematics
Volume	264
DOIs	https://doi.org/10.1016/j.aim.2014.07.016
State	Published - Oct 20 2014

Keywords

Cauchy integral
Linearly convex domains
Strongly pseudo-convex domains
Szego projection
T(1) theorem

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.aim.2014.07.016

Cite this

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title = "The Cauchy integral in Cn for domains with minimal smoothness",

abstract = "We prove Lp(bD)-regularity of the Cauchy-Leray integral for bounded domains D C Cn whose boundary satisfies the minimal regularity condition of class C1,1, together with a naturally occurring notion of convexity.",

keywords = "Cauchy integral, Linearly convex domains, Strongly pseudo-convex domains, Szego projection, T(1) theorem",

author = "Loredana Lanzani and Stein, {Elias M.}",

year = "2014",

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AU - Stein, Elias M.

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Y1 - 2014/10/20

N2 - We prove Lp(bD)-regularity of the Cauchy-Leray integral for bounded domains D C Cn whose boundary satisfies the minimal regularity condition of class C1,1, together with a naturally occurring notion of convexity.

AB - We prove Lp(bD)-regularity of the Cauchy-Leray integral for bounded domains D C Cn whose boundary satisfies the minimal regularity condition of class C1,1, together with a naturally occurring notion of convexity.

KW - Cauchy integral

KW - Linearly convex domains

KW - Strongly pseudo-convex domains

KW - Szego projection

KW - T(1) theorem

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