Course Descriptions

16:640:521 - Harmonic Analysis

Sagun Chanillo

Course Description:

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.

Text:

None

Prerequisites:

Math 501, 502, 503.

Schedule of Sections: