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

Abstract

We prove $L^p(bD)$-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.

51 pages

References in corpus (1)

• Cauchy-type integrals in several complex variables

Cited by in corpus (3)

• Sharp estimates for the Szegő projection on the distinguished boundary of model worm domains
• The Leray transform: factorization, dual $CR$ structures and model hypersurfaces in $\mathbb{C}{\mathbb{P}}^2$
• Irregularity of the Bergman projection on smooth unbounded worm domains