### Math 633. Harmonic Analysis: Fourier Analysis

- Spring 19 -
Hans Lindblad

The lectures are TuTh 10.30-11.45 in Shaffer 303.

We will to a large extent follow the lecture notes of Terry Tao:
Math 247A
and
Math 247B

We will at times also pick material from the book
Muscat, Schlag: Classical and Multilinear Harmonic Analysis Vol I and II
as well as from Hormander's books, Linear partial differential operators
and Lectures on nonlinear hyperbolic differential equations

My goal is really that we should learn the harminic analysis needed in apllications to
fluid mechnics in the paper
Germain, Masmoudi and Shatah: Global solutions for the gravity water waves equation in dimension 3
and to realtivity in the paper
D. Tataru and M. Tohaneanu: Local energy estimate on Kerr black hole backgrounds

This means the
Coifman-Meyer's estimate for bilinear fourier multipliers and the so called T(1) theorem,
for the fluid paper and the Weyl calculus for psedudifferential operators and Gardning's
inequality for the relativity paper.

There are also