@article{7f07486a06e74bf7ae05d221f20f1653,
title = "Regularity of a ∂¯ -Solution Operator for Strongly C -Linearly Convex Domains with Minimal Smoothness",
abstract = "We prove regularity of solutions of the ∂¯ -problem in the H{\"o}lder–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.",
keywords = "Homotopy formula, Lipschitz estimates, Strongly C-linear convexity",
author = "Xianghong Gong and Loredana Lanzani",
note = "Funding Information: Part of this work was carried out while the second-named author was in residence at the Isaac Newton Institute for Mathematical Sciences during the program Complex Analysis: techniques, applications and computations (EPSRC Grant No. EP/R04604/1). We thank the Institute, and the program organizers, for the generous support and hospitality. Finally, we are grateful to the referee for making several suggestions that have greatly improved the exposition. Funding Information: Partially supported by the National Science Foundation (DMS 1504589; DMS-1901978) and an INI-Simons fellowship. Funding Information: Partially supported by a grant from the Simons Foundation (Award No.: 505027). Publisher Copyright: {\textcopyright} 2020, Mathematica Josephina, Inc.",
year = "2020",
doi = "10.1007/s12220-020-00443-w",
language = "English (US)",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
}