Integral representations on non-smooth domains

We derive integral representations for $(0,q)$-forms, $q\ge 1$, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains. A $(0,q)$-form, $f$ is written in terms of integral operators acting on $f$, $\text{mdbar}f$, and ${\text{mdbar}}^{\ast }f$. The representation is applied to derive $L^{\mathrm{\infty }}$ estimates.