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

Abstract

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