The Cauchy integral in Cn for domains with minimal smoothness

Loredana Lanzani and Elias M. Stein

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

Journal: Advances in Mathematics, Volume 264, 2014, Pages 776–830

DOI: 10.1016/j.aim.2014.07.016