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

主题领域是多线性奇异积分和一些相关的极大算子，特别强调那些关于调制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。这一领域的一个显著特点是波包技术的使用，其根源可以追溯到大约40年前L.Carleson和C.Fefferman关于傅立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，几乎没有人感觉到这些技术的使用。正是在那时，M.Lacey和C.Thiele使用了相关的技术来解决A.Calderon关于双线性Hilbert变换的一个长期存在的猜想。经过相当多的数学家的努力，现在人们知道，这些技术对于研究一大类多线性奇异积分和极大算子是至关重要的。这些讲座的时机是在已经有了一系列复杂的结果时进行的，这些结果是一个美丽理论的新迹象。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，该学科的主要研究人员还将进行几次额外的讲座。

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.