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.
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Math 501, 502, 503.