Math 247B (Harmonic Analysis).

Lectures: MWF 10:00-10:50am in MS 6627.

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

Office Hours: Tu 1:30-2:30pm and Fri 1:30-2:30pm in MS 6167.

Topics:

Concentration compactness for the Gagliardo-Nirenberg and Sobolev embedding inequalities.
Existence of optimizers for Sobolev embedding.
The Kakeya problem.
Restriction theory beyond L².
Concentration compactness for the Schrodinger propagator.
Optimizers for the Strichartz inequality.

References:

J. Bourgain, Besicovitch type maximal operators and applications to Fourier analysis. GAFA 1 (1991), 147-187.
R. Killip and M. Visan, Nonlinear Schrodinger equations at critical regularity. To appear in Clay Mathematics Institute Summer School Proceedings.
E. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series, 43. Princeton University Press, 1993.
T. Tao, Restriction theorems and applications.
T. Wolff, Lectures on harmonic analysis. University Lecture Series, 29. American Mathematical Society, Providence, RI, 2003.

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.