NSF/CBMS Regional Conference in the Mathematical Sciences: Wave Packets, Multilinear Operators and Carleson Theorems; May 23-28, 2004; Atlanta, GA

NSF/CBMS 数学科学区域会议：波包、多线性算子和卡尔森定理；

• 批准号: 0332476
• 负责人: Gerd Mockenhaupt
• 金额: $ 3.2万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-05-01 至 2005-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0332476&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

The subject area is in the area of multilinear singular integrals, and some related maximal operators, with a particular emphasis on those with some invariance properties with respect to modulations. This is a new branch of Harmonic Analysis that has arisen within the last decade.A distinguishing feature of this area is the use of wave packet techniques which have roots going back to seminal work on convergence of Fourier series by L. Carleson, and C. Fefferman about 40 years ago. Yet the use of these techniques was hardly felt outside the subject of convergence of Fourier series until 1995. It was then that M. Lacey and C. Thiele used related techniques to a long standing conjecture of A. Calderon concerning the bilinear Hilbert transform.It is now understood, through the efforts of a sizable number of mathematicans, that these techniques are crucial to the study a wide class of multilinear singular integral and maximal operators. The timing of these lectures occurs when there is already a body of sophisticated results, from which are emerging signs of a beautiful theory. Connections to other fields of mathematics are at the horizon.Professor Thiele's will present this recent development in a series of lectures and there will be a few additional lectures by leading researchers in the subject.

主题领域是多线性奇异积分和一些相关的极大算子，特别强调那些在调制方面具有某些不变性的算子。 这是近十年来出现的调和分析的一个新分支。该领域的一个显着特征是波包技术的使用，其根源可以追溯到大约 40 年前 L. Carleson 和 C. Fefferman 在傅里叶级数收敛方面的开创性工作。然而，直到 1995 年，这些技术的使用才在傅立叶级数收敛性主题之外才被感受到。就在那时，M. Lacey 和 C. Thiele 使用了相关技术来解决 A. Calderon 关于双线性希尔伯特变换的长期猜想。现在，通过相当多的数学家的努力，人们了解到，这些技术对于研究一类广泛的多线性奇异积分和 最大运算符。这些讲座的时机发生在已经有大量复杂结果的时候，其中正在浮现出美丽理论的迹象。 与其他数学领域的联系即将到来。蒂勒教授将在一系列讲座中介绍这一最新进展，并且还将由该主题的领先研究人员进行一些额外的讲座。