English

Regularity of a $\bar\partial$-solution operator for strongly $\mathbf C$-linearly convex domains with minimal smoothness

Complex Variables 2021-01-26 v2

Abstract

We prove regularity of solutions of the ˉ\bar\partial-problem in the H\"older-Zygmund spaces of bounded, strongly C\mathbf C-linearly convex domains of class C1,1C^{1,1}. The proofs rely on a new, analytic characterization of said domains which is of independent interest, and on techniques that were recently developed by the first-named author to prove estimates for the ˉ\bar\partial-problem on strongly pseudoconvex domains of class C2C^2.

Keywords

Cite

@article{arxiv.1911.06203,
  title  = {Regularity of a $\bar\partial$-solution operator for strongly $\mathbf C$-linearly convex domains with minimal smoothness},
  author = {Xianghong Gong and Loredana Lanzani},
  journal= {arXiv preprint arXiv:1911.06203},
  year   = {2021}
}

Comments

19 pages. The authors improve the exposition of the proof of Proposition 2.5 of this paper which has been published in JGEA