The Cauchy-Riemann equations on product domains

被引：29

作者：

Chakrabarti, Debraj ^{[1
]}

Shaw, Mei-Chi ^{[1
]}

机构：

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

来源：

MATHEMATISCHE ANNALEN | 2011年 / 349卷 / 04期

基金：

美国国家科学基金会;

关键词：

DERIVATIVE-NEUMANN PROBLEM; BERGMAN PROJECTION; REGULARITY;

D O I：

10.1007/s00208-010-0547-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the L (2) theory for the Cauchy-Riemann equations on product domains provided that the Cauchy-Riemann operator has closed range on each factor. We deduce regularity of the canonical solution on (p, 1)-forms in special Sobolev spaces represented as tensor products of Sobolev spaces on the factors of the product. This leads to regularity results for smooth data.

引用

页码：977 / 998

页数：22

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