English

Optimal H\"{o}lder regularity for the $\bar\partial$ problem on product domains in $\mathbb C^2$

Complex Variables 2021-03-09 v1

Abstract

The note concerns the ˉ\bar\partial problem on product domains in C2\mathbb C^2. We show that there exists a bounded solution operator from Ck,αC^{k, \alpha} into itself, kZ+{0},0<α<1k\in \mathbb Z^+\cup \{0\}, 0<\alpha< 1. The regularity result is optimal in view of an example of Stein-Kerzman.

Keywords

Cite

@article{arxiv.2103.04517,
  title  = {Optimal H\"{o}lder regularity for the $\bar\partial$ problem on product domains in $\mathbb C^2$},
  author = {Yuan Zhang},
  journal= {arXiv preprint arXiv:2103.04517},
  year   = {2021}
}
R2 v1 2026-06-23T23:51:39.979Z