\(\mathcal C^k\)-estimates for the Cauchy-Riemann operator on domains with \(q\)-convex and \(q\)-concave edges
type: Item
instance of: scholarly article
title: \(\mathcal C^k\)-estimates for the Cauchy-Riemann operator on domains with \(q\)-convex and \(q\)-concave edges
zbMATH Open document ID: 1036.32012
author: Hélène Ricard
published in: Mathematische Zeitschrift
publication date: 2003-08-17T00:00:00Z
review text: In this highly technical paper, \({\mathcal C}^k\) estimates for the solutions of the \(\overline\partial\) CR equation are established for \(q\)-convex edges. This sharpens previous estimates by \textit{M.-Y. Barkatou} [Math. Z. 239, No. 2, 335--352 (2002; Zbl 1006.32031)]. Then analogous estimates for \(q\)-concave edges are provided. From these results, a result for local resolution with regularity up to the boundary, on the complement \(W\) of a \(q\)-convex domain \(D\) with \({\mathcal C}^d\) piecewise boundaries is given. This provides some improvement of earlier results by Laurent-Thiebault andLeiterer. Finally, the author establishes a global resolution result for \((0, r)\)-forms with compact support on the complement of a strictly \(q\)-convex domain \(\Omega\Subset X\) with piecewise smooth boundaries. This gives a generalization to the separation theorem by Andreotti and Vesentini.
reviewed by: Tan Vovan
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 1965495
zbMATH Keywords: \({\mathcal C}^k\) estimates
zbMATH Keywords: CR equation
zbMATH Keywords: convex edges
zbMATH Keywords: \(q\)-concave edges
MaRDI profile type: Publication
full work available at URL: s00209-003-0504-4
OpenAlex ID: W2130817490
DOI: 10.1007/S00209-003-0504-4
description: scientific article; zbMATH DE number 1965495