Hardy spaces of differential forms and applications

微分形式的 Hardy 空间及其应用

• 批准号: LX0348151
• 负责人: Prof Alan McIntosh
• 金额: $ 1.32万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Linkage - International
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-06-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/LX0348151
• 关键词: Hardy; spaces; differential; forms; applications

Hardy spaces on Euclidean spaces were developed in the 1970's following the fundamental work of Stein, Weiss and Fefferman. These spaces play an important role in harmonic analysis, as they are the natural spaces on which to consider singular integral operators. They arise in many contexts, such as when using Jacobians in non-linear partial differential equations. Recently the French participants and the Australian participants have have obtained different but related results concerning Hardy spaces of exact differential forms. The time is now ripe to construct a unified theory.

欧氏空间上的Hardy空间是在Stein，Weiss和Fefferman的基础工作之后，在20世纪70年代的S发展起来的。这些空间在调和分析中起着重要的作用，因为它们是考虑奇异积分算子的自然空间。它们出现在许多情况下，例如在非线性偏微分方程中使用雅可比时。最近，法国的参与者和澳大利亚的参与者得到了关于精确微分形式的Hardy空间的不同但相关的结果。构建一个统一理论的时机现在已经成熟。