Analysis IV
Math 2304 Spring 2009
MWF 3:00-3:50 pm, 524 Thackeray Hall
Instructor: Piotr Hajlasz
Office: 622 Thackeray Hall
Email: hajlasz@pitt.edu
Textbook: Lecture notes that will be available online.
Course Grade: Homework (100%)
Office Hours: MW 4:30-5:30pm 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,
multiplier theorems
(the Marcinkiewicz and the Hormander theorems)
BMO,
Hardy space,
Fefferman duality theorem,
Muckenhoupt weights,
Bessel and Riesz potentials with applicatations to Sobolev spaces.
Lecture notes:
Harmonic Analysis
Check for new versions regularly.
Other useful sources:
Functional Analysis
Measure Theory
Homework:
HW#1 Due February 2.
HW#2 Due February 9.
HW#3 Due February 27.
HW#4 No due date yet.
HW#5 No due date yet.