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

本课程的主题是多元线性奇异积分，以及一些相关的极大算子，特别强调那些在调制方面具有不变性的算子。这是近十年来谐波分析的一个新分支。该领域的一个显著特征是使用波包技术，其根源可以追溯到大约40年前L. Carleson和C. Fefferman关于傅里叶级数收敛的开创性工作。然而，直到1995年，在傅里叶级数收敛的主题之外，这些技术的使用几乎没有被感觉到。就在那时，莱西（Lacey）和蒂勒（C. Thiele）用相关的技术来证明卡尔德隆（a . Calderon）关于双线性希尔伯特变换的一个长期存在的猜想。现在，通过相当数量的数学家的努力，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算子和极大算子是至关重要的。这些讲座的时机是在已经有一系列复杂结果的时候，从这些结果中可以看出一个美丽理论的迹象。与其他数学领域的联系正在出现。蒂勒教授将在一系列讲座中介绍这一最新进展，并将由该学科的主要研究人员进行一些额外的讲座。

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.