H\"older regularity of the $\bar\partial-$equation on the polydisc
Complex Variables
2026-02-05 v2 Analysis of PDEs
Abstract
In this note, we show the existence of a solution operator to the equation in the polydisc that preserves H\"older regularity. This solution operator is constructed using Henkin's formula. It is a well-known fact that solution operators to the equation on product domains do not improve H\"older regularity. Hence, this solution operator is optimal in that regard.
Cite
@article{arxiv.2301.04484,
title = {H\"older regularity of the $\bar\partial-$equation on the polydisc},
author = {Yu Jun Loo and Alexander Tumanov},
journal= {arXiv preprint arXiv:2301.04484},
year = {2026}
}