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

19 pages. The error in section 4 in the previous version has been fixed. A couple sections have been rewritten

References in corpus (2)

• Bergman subspaces and subkernels: Degenerate $L^p$ mapping and zeroes
• An Integral Kernel for Weakly Pseudoconvex Domains