An Ode to Stein: N lectures in harmonic analysis

This is a short course on the basic tools in harmonic analysis covering the following topics (in order):

1. The Hardy--Littlewood maximal function and Birkhoff's ergodic theorem (First draft of notes below) [2019.02.13]
2. The Hilbert transform and singular integrals [2019.02.27 by Ed, 03.06, 03.13]
3. Basics of the Fourier transform [2019.03.20, 04.03, 04.24]
4. Littlewood--Paley theory [2019.05.01, 5.08, 5.22, 5.29]
5. Variations of averages - cancelled due to time constraints
6. Oscillatory integrals - cancelled due to time constraints

The main reference for the course are T. Tao's notes on Fourier analysis which can be found here and here. With respect to these notes, I will assume knowledge of Notes 1, and cover material in Notes 2,3, and 4 and 8. In particular, I will assume familiarity with L^p spaces and interpolation. Other useful references include Stein and Shakarchi's Fourier Analysis and their Real Analysis and their Functional Analysis as well as Stein's Harmonic analysis and Singular integrals, and Stein and Weiss's Introduction to Fourier Analysis on Euclidean Spaces. I also encourage you to look at these notes by Lerner and Nazarov which have a more modern take on these classical topics. There are many other great texts and I do not intend to omit them - I only do out of ignorance. Some others include Grafakos's book, Mascalu and Schlag's book, Katznelson's book and Zygmund's trigonometric series. The fourth topic follows closely some notes of Klainerman.

My own notes are posted here. Use with caution as they are currently in a rough state. Comments and corrections on my notes are welcome :)

A secondary purpose of this course is as a preparatory course for a subsequent course (possibly in the Spring of 2020) on arithmetic analogues in harmonic analysis. This future course will discuss arithmetic versions of the above topics.

It appears that N was 11.