Mathematical Sciences: Weighted Norm Inequalities and Applications

数学科学：加权范数不等式及其应用

• 批准号: 9500799
• 负责人: Richard Wheeden
• 金额: $ 10.5万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500799&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Weighted; Norm; Inequalities

Wheeden DMS-9500799 The research will investigate the role of weighted norm inequalities in harmonic analysis and differential equations. The emphasis is to study questions that arise naturally in these subjects, and to obtain conditions on the weights or measures which are as sharp and simple to verify as possible, and which reflect the particular nature of the situation being studied. The problems are related to finding weighted norm estimates between a function and various transforms of the function. Mathematical research in harmonic analysis seeks to study the fine structure of mathematical functions and their underlying domains of definition. The tools developed by this work bring out hidden relationships not ordinarily detected by more classical methods.

Wheeden DMS-9500799这项研究将调查加权范数不等在调和分析和微分方程中的作用。重点是研究这些科目中自然出现的问题，并获得有关度量衡的条件，这些条件应尽可能尖锐和简单，以便于验证，并反映所研究情况的特殊性质。这些问题涉及到在函数和函数的各种变换之间寻找加权范数估计。调和分析中的数学研究致力于研究数学函数的精细结构及其定义的基本领域。这项工作开发的工具揭示了更经典的方法通常不能检测到的隐藏关系。