Integral representations on non-smooth domains

TL;DR

This paper develops integral formulas for (0,q)-forms on non-smooth strictly pseudoconvex domains, enabling new $L^{ olinebreak}^ olinebreak$ estimates and advancing analysis on complex domains with boundary irregularities.

Contribution

It introduces integral representations for (0,q)-forms on non-smooth domains, extending classical methods to Henkin-Leiterer domains with boundary singularities.

Findings

Derived integral representations for (0,q)-forms on non-smooth domains.

Applied representations to obtain $L^{ olinebreak}^ olinebreak$ estimates.

Extended classical complex analysis techniques to irregular boundary domains.

Abstract

We derive integral representations for $(0,q)$-forms, $q\ge1$, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains. A $(0,q)$-form, $f$ is written in terms of integral operators acting on $f$, $\mdbar f$, and $\mdbar^{\ast} f$. The representation is applied to derive $L^{\infty}$ estimates.