Extendability and the (partial derivative)over-bar operator on the Hartogs triangle

被引：0

作者：

Burchard, Almut ^{[1
]}

Flynn, Joshua ^{[2
,3
]}

Lu, Guozhen ^{[2
,3
]}

Shaw, Mei-Chi ^{[3
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

[2] Univ Connecticut, Dept Math, Storrs, CT 06290 USA

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

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 301卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

PSEUDO-CONVEX MANIFOLDS; HARMONIC INTEGRALS; REGULARITY; DOMAINS; COMPLEX; BOUNDARY;

D O I：

10.1007/s00209-022-03008-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper it is shown that the Hartogs triangle T in C-2 is a uniform domain. This implies that the Hartogs triangle is a Sobolev extension domain. Furthermore, the weak and strong maximal extensions of the Cauchy-Riemann operator agree on the Hartogs triangle. These results have numerous applications. Among other things, they are used to study the Dolbeault cohomology groups with Sobolev coefficients on the complement of T.

引用

页码：2771 / 2792

页数：22

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