Topics in Harmonic Analysis Math 3460 Spring 2013

MWF 1:00-1:50 pm, 230 Cathedral of Learning

Instructor: Piotr Hajlasz

Office: 420 Thackeray Hall

Email: hajlasz@gmail.com

Course Grade: Homework (100%)

Office Hours: M 4:00-5:00 pm W 6:00-7:00 pm and by appointment

What is it about? This is a basic course in Harmonic Analysis on the Euclidean space. The following topics will be covered: Fourier transform, tempered distributions, interpolation (the Marcinkiewicz and the Riesz-Thorin theorems) maximal functions, spherical harmonics, Hilbert transform, singular integrals, Riesz transforms, Calderon-Zygmind theory, Littlewood-Paley theory, Stein spherical maximal theorem.

Textbook: Lecture notes that will be available online.

Harmonic Analysis

Additional materials in Harmonic Analysis

Other useful textbooks:

E.M. Stein, Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970 xiv+290 pp.

L. Grafakos, Modern Fourier analysis. Second edition. Graduate Texts in Mathematics, 250. Springer, New York, 2009. xvi+504 pp. ISBN: 978-0-387-09433-5

L. Grafakos, Classical Fourier analysis. Second edition. Graduate Texts in Mathematics, 249. Springer, New York, 2008. xvi+489 pp. ISBN: 978-0-387-09431-1

J. Duoandikoetxea, Fourier analysis. Graduate Studies in Mathematics, 29. American Mathematical Society, Providence, RI, 2001. xviii+222 pp. ISBN: 0-8218-2172-5

Other useful sources:

Functional Analysis

Measure Theory

Homework:

I will not return the homework, so it is a good to keep a copy. 10% bonus for solutions written in LaTeX. You must learn LaTeX, so if you do not know it yet, it is a good moment to start.

HW#1 Due date Friday February 8.

HW#2 Due date Friday March 1.

HW#3 Due date Friday March 18.

HW#4 Due date Friday March 29.

HW#5 Due date Friday April 5.

HW#6 Due date Friday April 12.