Mathematical Sciences: Multi-Parameter Harmonic Analysis andLittlewood-Paley Inequalities

数学科学：多参数调和分析和Littlewood-Paley 不等式

• 批准号: 8811775
• 负责人: James Michael Wilson
• 金额: $ 1.75万
• 依托单位: University of Vermont & State Agricultural College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-02-15 至 1991-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8811775&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multi; Parameter; Harmonic

Work to be done on this project will focus on problems arising in the modern theory of harmonic analysis and its relationship with partial differential equations. This relationship arises naturally when differential equations are transformed by various means into integral expressions or operators. In 1976, the fundamental inequalities relating bounds of Calderon-Zygmund operate to weighted function norms were obtained. Extensive work on these estimates followed, but most work was confined to one-parameter operators. In this project, a multiparameter theory is laid out for investigation. The basic inequalities are much harder to achieve in this context because of the complexities of higher dimentional analogues to dyadic intervals. Nevertheless, inequalities have been established for the two parameter case. Applications are to be made to elliptic operators such as two-parameter Schrodinger operators and the development of a correspondinguncertainty principle.

该项目要做的工作将集中于现代调和分析理论中出现的问题及其与偏微分方程的关系。 当微分方程通过各种方式转化为积分表达式或运算符时，这种关系自然会出现。 1976 年，获得了有关 Calderon-Zygmund 的界与加权函数范数相关的基本不等式。 随后对这些估计进行了大量工作，但大多数工作仅限于单参数运算符。 在该项目中，提出了多参数理论进行研究。 在这种情况下，由于二元区间的高维类似物的复杂性，基本的不等式更难实现。 然而，对于两个参数的情况已经建立了不等式。 将应用于椭圆算子，例如二参数薛定谔算子，并开发相应的不确定性原理。