Extendability and the $\overline \partial$ Operator on the Hartogs Triangle
Complex Variables
2022-01-31 v2
Abstract
In this paper it is shown that the Hartogs triangle in is a uniform domain. This implies that the Hartogs triangle is a Sobolev extension domain. Furthermore, the weak and strong maximal extensions of the Cauchy-Riemann operator agree on the Hartogs triangle. These results have numerous applications. Among other things, they are used to study the Dolbeault cohomology groups with Sobolev coefficients on the complement of .
Cite
@article{arxiv.2106.09867,
title = {Extendability and the $\overline \partial$ Operator on the Hartogs Triangle},
author = {Almut Burchard and Joshua Flynn and Guozhen Lu and Mei-Chi Shaw},
journal= {arXiv preprint arXiv:2106.09867},
year = {2022}
}
Comments
Accepted for publication in Math. Zeit.; 23 pages, typos corrected