MATH 242, Fall 2017
Topics in Harmonic Analysis

Meeting time/location: Mo 8-8:50am, Fr: 11:15am-1:50pm in AP&M 5829.

Instructor: Ioan Bejenaru

Office: AP&M 5111
Office Hours: by appointment

Textbook: "Classical Fourier Analysis" by Loukas Grafakos. The UCSD library makes the book available electronically.

Additional reading: "Harmonic Analysis" by Elias Stein, Terence Tao's notes .

We will cover the following topics:
Fourier transform in classical and distributional sense, Calderon-Zygmund theory for singular integral operators,
Sobolev spaces using Riesz and Bessel potentials, Littlewood-Paley theory, Oscillatory integrals and applications,
Applications to Partial Differential Equations.

Homework will be assigned biweekly. Working on the Homework is optional.

Notes: Introduction, Basic Real Analysis, The Fourier transform , The Calderon-Zygmund theory, multiplier theory , Riesz and Bessel potentials, Sobolev and Lipschitz spaces.

HW 1: 2.2: 1,2,5,8,13; 2.3: 1,4,6(this would require a bit more reading from Grafakos),9,10,11
HW 2: 4.3: 1,2,9; from Tao's notes (#4): Q1,Q2,Q4,Q10
HW 3: 6.2: 1,2,3,5,8,9,12