The Cauchy Integral in \mathbb Cⁿ for domains with minimal smoothness

2013/11/20 by Loredana Lanzani, Elias M. Stein, Lanzani, Loredana +1
Mathematics · #30E20 #31A10 #31B10 #32A25 #32A26 #32A50 #32A55 #42B20 #46E22 #47B34 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:30E20 #msc:31A10 #msc:31B10 #msc:32A25 #msc:32A26 #msc:32A50 #msc:32A55 #msc:42B20 #msc:46E22 #msc:47B34

paper · pdf · doi:10.48550/arxiv.1311.5167

50 pages, 1 figure

arxiv created 2013/11/20 · openalex publication_date 2013/11/20 · arxiv updated 2013/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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