Boundedness of Singular integral operators and applications to Bochner-Riesz summability, Riesz transforms, and Hardy spaces.

奇异积分算子的有界性以及 Bochner-Riesz 可求和性、Riesz 变换和 Hardy 空间的应用。

• 批准号: DP0344688
• 负责人: Prof Xuan Thinh Duong
• 金额: $ 12.89万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2006-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0344688
• 关键词: Boundedness; Singular; integral; operators; applications

We aim to develop harmonic analysis methods to study singular integral operators and function spaces associated to these operators. We propose to study the long standing problem of convergence of Bochner-Riesz means in Fourier analysis, and investigate differential operators with non-smooth coefficients acting on rough domains, or acting on general spaces like manifolds. Expected outcomes are new techniques in harmonic analysis to be developed, with applications being solutions to a number of open problems in the theories of harmonic analysis, partial differential equations and function spaces.

我们的目标是发展调和分析方法来研究奇异积分算子和与这些算子相关的函数空间。我们提出研究傅立叶分析中Bochner-Riesz平均的收敛性问题，并研究作用在粗糙域或流形等一般空间上的非光滑系数微分算子. 预期的成果是新的技术在调和分析开发，应用程序是解决一些开放的问题，在调和分析，偏微分方程和函数空间的理论。