Topics in Harmonic Analysis


Course Meeting Time and Location
Tuesday and Thursday
2:30 - 3:55 pm
104 Math Building (Building 15)


Course Instructor Contact Information and Office Hours
122 Math Building (Building 15)
E-mail: durcik at caltech dot edu
Office hours: By appointment


Course Description
We will discuss some topics from classical and multilinear harmonic analysis.
Related keywords are paraproducts, T(1) and T(b) theorems.


Prerequisites: The Fourier transform, Lp spaces.

References:

J.
Duoandikoetxea: Fourier Analysis
C. Muscalu and W. Schlag: Classical and Multilinear Harmonic Analysis


Papers:
1.  V. Kovac: Boundedness of the twisted paraproduct
2.  P. D., V. Kovac, K. A. Skreb, C. Thiele: Norm-variation of ergodic averages with respect to two commuting transformations
3.  V. Kovac, C. Thiele: A T(1) theorem for entangled multilinear dyadic Calderon-Zygmund operators
4.  M. Mirek, C. Thiele: A local T(b) theorem for perfect multilinear Calderon-Zygmund operators



Course Policies
In the first half of the course we will review some topics from the linear Calderon-Zygmund theory. We will discuss the classical T(1) theorem and then move on to paraproducts. The second half of the course will be structured as a reading course. In the first week of April the participants will choose a paper from the above list, which they will present in class. Each participant will give two 60 min lectures. The presentations will start in May. The schedule is announced below.

Course schedule