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

Liwei Chen; Jeffery McNeal

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

Complex Variables 2018-09-24 v4

Authors: Liwei Chen , Jeffery McNeal

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.

Keywords

operator theory and elliptic operators operator theory

Cite

@article{arxiv.1710.04704,
  title  = {A solution operator for $\bar\partial$ on the Hartogs triangle and $L^p$ estimates},
  author = {Liwei Chen and Jeffery McNeal},
  journal= {arXiv preprint arXiv:1710.04704},
  year   = {2018}
}

Comments

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

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