Speaker: Loukas Grafakos (University of Missouri at Columbia)

Title: The role of Gabor wavelets in the Carleson-Hunt theorem on almost everywhere convergence of the Fourier series


A maximal dyadic sum operator which models the Carleson-Hunt operator using Gabor wavelets will be discussed. The proof of boundedness of this operator will be outlined and the role of the Gabor wavelets will be explained. An improved energy estimate for Bessel-type expressions associated with Gabor wavelets will be crucial in obtaining the boundedness of these operators.