Regularity of a ∂¯ -Solution Operator for Strongly C -Linearly Convex Domains with Minimal Smoothness

Xianghong Gong, Loredana Lanzani

Research output: Contribution to journalArticle

Abstract

We prove regularity of solutions of the ∂¯ -problem in the Hölder–Zygmund spaces of bounded, strongly C-linearly convex domains of class C1 , 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 ∂¯ -problem on strongly pseudoconvex domains of class C2.

Original languageEnglish (US)
JournalJournal of Geometric Analysis
DOIs
StateAccepted/In press - 2020

Keywords

  • Homotopy formula
  • Lipschitz estimates
  • Strongly C-linear convexity

ASJC Scopus subject areas

  • Geometry and Topology

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