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

Abstract

We prove regularity of solutions of the $\bar{\partial }$-problem in the Hölder-Zygmund spaces of bounded, strongly $\mathbf{C}$-linearly convex domains of class $C^{1,1}$. 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 $\bar{\partial }$-problem on strongly pseudoconvex domains of class $C^2$.

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