The Cauchy Integral in ${\mathbb{C}}^n$ for domains with minimal smoothness

Abstract

We prove $L^p(b\mathcal{D})$-regularity of the Cauchy-Leray integral for bounded domains $\mathcal{D}\subset {\mathbb{C}}^n$ whose boundary satisfies the minimal regularity condition of class $C^{1,1}$, together with a naturally occurring notion of convexity.

50 pages, 1 figure