Non-closed Range Property for the Cauchy-Riemann Operator

被引：6

作者：

Laurent-Thiebaut, Christine ^{[1
,2
]}

Shaw, Mei-Chi ^{[3
]}

机构：

[1] Univ Grenoble Alpes, IF, F-38000 Grenoble, France

[2] CNRS, IF, F-38000 Grenoble, France

[3] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

来源：

ANALYSIS AND GEOMETRY | 2015年 / 127卷

关键词：

Cauchy-Riemann operator; Closed range; Duality; REGULARITY; MANIFOLDS; DOMAINS; COHOMOLOGY; EQUATION; EXAMPLE; DUALITY;

D O I：

10.1007/978-3-319-17443-3_11

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the non-closed range of the Cauchy-Riemann operator for relatively compact domains in C-n or in a complex manifold. We give necessary and sufficient conditions for the L-2 closed range property for. on bounded Lipschitz domains in C-2 with connected complement. It is proved for the Hartogs triangle that. does not have closed range for (0, 1)-forms smooth up to the boundary, even though it has closed range in the weak L-2 sense. An example is given to show that. might not have closed range in L-2 on a Stein domain in complex manifold.

引用

页码：207 / 217

页数：11

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