Topics in Harmonic Analysis
Student No.:50
Time:Tue/Thu 10:10-12:00, 2015-07-02 ~ 2015-07-30
Instructor:Garving K. Luli  [University of California, Davis]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-7-2
Ending Date:2015-7-30




Harmonic analysis revolves around the study of the quantitative properties (e.g. boundedness, smoothness) of functions and how these properties change under certain kind of operators. It is a fundamental tool in the studies of partial differential equations, data analysis, imaging analysis, and many other areas. 

This course will examine some of the general themes in (modern) harmonic analysis. We will start by reviewing some basic tools in the subject, including the Hardy-Littlewood maximal function, Calderon- Zygmund decomposition, singular integrals, interpolation of function spaces, H1 and BMO. Then we will look at how these tools can be applied to the analysis of partial differential equations, restriction theorems, and extension theorems (a la Whitney). ”divide and conquer” (a.k.a. Calderon-Zygmund decomposition) will be a reoccurring theme in the course.





The prerequisites for the course are a basic course on real analysis and a working under- standing of measure theory. The lectures will be self-contained.




Some useful references for the course are ”Singular Integrals and Differentiability Properties of Functions” by E. Stein, ”Modern Fourier Analysis” by L. Grafakos.