Harmonic Analysis

3 Credits · Level: Graduate, Undergraduate

The first part of the course concentrates on some fundamental results in Fourier analysis (Bochner's theorem, Hardy-Littlewood maximal functions, Fefferman-Stein sharp functions, and the space of bounded mean oscillation) on Euclidean spaces. In the second part of this course, we are going to study singular integral operators through a few important example: Hilbert and Riesz transforms, the Szeg\{"}o projection operator on the Heisenberg group, and Cauchy integral on Lipschitz curves in the complex plane. Our goal is to explain some of the principal aspects of the great progress that has been made in the past thirty years or some toward understanding Calder\{'}on-Zygmund operators.