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

Xianghong Gong; Loredana Lanzani

doi:10.1007/s12220-020-00443-w

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

Xianghong Gong, Loredana Lanzani

Department of Mathematics

Research output: Contribution to journal › Article

Abstract

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

Original language	English (US)
Journal	Journal of Geometric Analysis
DOIs	https://doi.org/10.1007/s12220-020-00443-w
State	Accepted/In press - 2020

Keywords

Homotopy formula
Lipschitz estimates
Strongly C-linear convexity

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s12220-020-00443-w

Fingerprint Dive into the research topics of 'Regularity of a ∂¯ -Solution Operator for Strongly C -Linearly Convex Domains with Minimal Smoothness'. Together they form a unique fingerprint.

Cite this

Gong, X., & Lanzani, L. (Accepted/In press). Regularity of a ∂¯ -Solution Operator for Strongly C -Linearly Convex Domains with Minimal Smoothness. Journal of Geometric Analysis. https://doi.org/10.1007/s12220-020-00443-w

@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",

year = "2020",

doi = "10.1007/s12220-020-00443-w",

language = "English (US)",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer New York",

}

TY - JOUR

T1 - Regularity of a ∂¯ -Solution Operator for Strongly C -Linearly Convex Domains with Minimal Smoothness

AU - Gong, Xianghong

AU - Lanzani, Loredana

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Homotopy formula

KW - Lipschitz estimates

KW - Strongly C-linear convexity

UR - http://www.scopus.com/inward/record.url?scp=85087940037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85087940037&partnerID=8YFLogxK

U2 - 10.1007/s12220-020-00443-w

DO - 10.1007/s12220-020-00443-w

M3 - Article

AN - SCOPUS:85087940037

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

ER -