This course is a basic course on Harmonic Analysis. We will study, interpolation theorems the Hardy-Littlewood-Sobolev fractional integration theorem. Then Calderon-Zygmund theory of Singular integrals. After that we will prove the Hormander multiplier theorem. This will be followed by Littlewood-Paley theory. We will end with the study of Fourier transform restriction theorems, applications to the Strichartz estimates for wave and Schrodinger equations and the theory of Bochner-Riesz multipliers. This course is addressed to students who need these tools in Nonlinear analysis and PDE and in their study of elliptic, parabolic and hyperbolic problems.
Math 501, 502, 503.