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.

我们的目标是开发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。我们建议研究傅里叶分析中长期存在的 Bochner-Riesz 均值收敛问题，并研究作用于粗糙域或作用于流形等一般空间的非光滑系数微分算子。 预期成果是调和分析新技术的开发，其应用是调和分析、偏微分方程和函数空间理论中许多开放问题的解决方案。