**Instructor:** Monica Visan, MS 6167. Email address: visan@math.ucla.edu

**Office Hours:** Wed 1:00pm-2:00pm.

**Topics:**

- Basic properties of the Fourier transform in
**R**^{d}. - Maximal and vector maximal inequalities.
- Calderon-Zygmund singular integral operators.
- Littlewood-Paley theory.
- Fractional chain/product rules.
- Stationary phase.
- Rearrangement inequalities.

- E. Stein,
*Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals.*Princeton Mathematical Series, 43. Princeton University Press, 1993. - E. Stein,
*Singular integrals and differentiability properties of functions.*Princeton Mathematical Series, 30. Princeton University Press, 1970.

**Grading:** Grading will be based solely on the homework. Problems
will be assigned and collected throughout the quarter.

**Homework:** You may collaborate on the homework, but solutions need
to be written up in your own words.

- Homework 1: due on Friday, Feb. 10th.
- Homework 2: due on Friday, Mar. 3rd.
- Homework 3: due on Friday, Mar. 17th.