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 › peer-review

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

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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.",

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AU - Gong, Xianghong

AU - Lanzani, Loredana

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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

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