Integral representations on nonsmooth domains

Abstract

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