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

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

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.