## 16:640:521 Harmonic Analysis

## Fall 2020

### 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.

### Textbook:

None

### Prerequisites:

Math 501, 502, 503.