Qifan Li - The Carleson-Hunt theorem

Abstract:
The Carleson's famous paper in 1966 proved that the Fourier series of square-integrable functions converges almost everywhere. As indicated in Hunt's paper in 1967, Carleson's method can be modified to deal with the functions in L^p-space with p>1. In addition to Carleson's work, Fefferman provides another approach to solve this problem in 1971. His proof relies on the almost orthogonality property of the maximal Carleson operator on the time-frequency plane. This inspired the development of the theory of the time-frequency analysis. The joint paper of Lacey and Thiele in 2000 showed that the maximal Carleson operator can be decomposed in the time-frequency plane in terms of wave-packets and they provide a new proof of Carleson's theorem. We will follow the Carleson's approach in this talk and discuss the iteration arguments and the construction of exceptional sets.