__ Schedule of classes __:
T R 9:45 - 11:00 AM in 107 WILLARD.

__NO CLASSES__ OCTOBER 2-4, 2012.

EXTRA CLASSES: Tuesday September 18 and Tuesday December 11.
Both sessions held 5:30 - 6:45 PM in 315 McAllister.

__Office Hours (subject to change):__
TUESDAY 11 AM - 12:30 PM,
THURSDAY 5 - 6:30 PM.

**Textbook (optional)**J. Duoandikoetxea,

*Fourier analysis*, Graduate Studies in Mathematics, 29. American Mathematical Society, Providence, RI, 2001.

**Course Topics**:

- Fourier series and Fourier transform in $L^{1}$ and $L^{2}$: basic properties, inversion, summability methods (Gauss-Weierstrass, Abel), point-wise convergence (briefly);
- Schwartz space, tempered distributions, weak derivatives (review), principal-value distributions, Fourier transform on distributions;
- Interpolation of operators: weak $L^{p}$, Marcinkiewicz and Riesz-Thorin Theorems;
- Hardy-Littlewood maximal function and Calderon-Zygmund decomposition (via dyadic maximal function);
- Hilbert transform and Fourier multipliers on the real line;
- Singular integrals: convolution operator with odd homogeneous kernels, Riesz transforms, and method of rotations;

**Homework Problems**: solutions will be available on ANGEL (

*under the "lessons" tab*) roughly one week after the problems are posted.

- Homework 1, due THURSDAY SEPTEMBER 20.
- Homework 2, due THURSDAY OCTOBER 11.
- Homework 3, due THURSDAY OCTOBER 25.
- Homework 4, due THURSDAY NOVEMBER 8.
- Homework 5, due THURSDAY NOVEMBER 29.
- Homework 6, due TUESDAY DECEMBER 11.

© Anna Mazzucato Last modified: Tue Dec 4 12:20:52 EST 2012