A solution operator for $\bar{\mathrm{\partial }}$ on the Hartogs triangle and $L^p$ estimates

An integral solution operator for $\bar{\mathrm{\partial }}$ is constructed on product domains that include the punctured bidisc. This operator is shown to satisfy $L^p$ estimates for all $1\le p<\mathrm{\infty }$, though with non-standard – relative to strongly pseudoconvex domains – bounding term. These estimates imply $L^p$ estimates for $\bar{\mathrm{\partial }}$ on the Hartogs triangle, with greater range of $p$ than the canonical solution satisfies.