Weighted $C^k$ estimates for a class of integral operators on non-smooth domains

We apply integral representations for $(0,q)$-forms, $q\ge 1$, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $C^k$ estimates for a given $(0,q)$-form, $f$, in terms of $C^k$ norms of $\text{mdbar}f$, and ${\text{mdbar}}^{\ast }f$. The weights are powers of the gradient of the defining function of the domain.