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

Liwei Chen; Jeffery McNeal

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arXiv · 1710.04704

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

Liwei Chen·Jeffery McNeal

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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 $1\leq p <\infty$, 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.

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BibTeX RIS

Liwei Chen, Jeffery McNeal. 2018-09-20. A solution operator for $\bar\partial$ on the Hartogs triangle and $L^p$ estimates. https://arxiv.org/abs/1710.04704

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