Fall 2015, Math 890, Fourier Analysis
Course Information
This course introduces some topics in Fourier analysis on the Euclidean spaces.
We will use the book by E. Stein and G. Weiss, ``Introduction to Fourier Analysis on Euclidean
spaces". For background material, we recommend the book by G. Folland, ``Real Analysis:
Modern techniques and their applications". We tentatively plan to cover Chapter 1, 2, 4
in Stein and Weiss' book. More precisely, the topics are
1. The L^1 and L^2 theory of the Fourier transform.
2. The Schwartz class and the tempered distributions.
3. Introduction to harmonic and subharmonic functions, and characterization of Poisson integrals.
4. The HardyLittleowood maximal function and boundary values of harmonic functions.
5. Spherical harmonics and a decomposition of L^2 into Fourierinvariant subspaces.
6. The Fourier transform of P(x)/x^{n+k\alpha}, where 0\le \alpha< n and P(x)
is a harmonic polynomial of degree k, and the principal value distributions.
If time permits, we will discuss the interpolation theory of operators in L^p
spaces and Lorentz spaces.

Time: MWF 1:00  1:50 PM

Location: Snow Hall 456

Text: Introduction to Fourier Analysis on Euclidean Spaces, By E. Stein and
G. Weiss
 Instructor: Shuanglin Shao
 Office: Snow Hall 615
 Email: slshao@ku.edu
 Office Hour: MWF: 2:00  3:00 PM, or by appointment.
Miscellaneous
There will be no exams in this course. There are 3 or 4 homework assignments
throughout the course.
Homework 890.