  Let $\Omega\subset\mathbb{C}^n$ be a product of one-dimensional open bounded
domains with $C^{1,\alpha}$ boundary, where $0<\alpha<1$. Using methods from
complex analysis in one variable, we construct an integral operator that solves
$\bar\partial$ in $\Omega$ with supnorm estimates when the datum is in
$C^{n-1,\alpha}(\Omega)$.
