The Cauchy-Szeg\H o projection for domains in $\mathbb C^n% with minimal smoothness

TL;DR

This paper establishes the $L^p$ regularity of the Cauchy-Szeg o projection on bounded domains in complex space with minimal $C^2$ boundary regularity and a convexity condition.

Contribution

It proves the $L^p$ regularity of the Cauchy-Szeg o projection for domains with only $C^2$ boundary smoothness, extending previous results.

Findings

$L^p$ regularity holds for $1 < p < \infty$

Results apply to domains with minimal smoothness and convexity

Advances understanding of boundary regularity in several complex variables

Abstract

We prove $L^p(b D)$-regularity of the Cauchy-Szeg\H o projection (also known as the Szeg\H o projection) for bounded domains $D\subset\mathbb C^n$ whose boundary satisfies the minimal regularity condition of class $C^2$, together with a naturally occurring notion of convexity.