MA8106 Harmonic Analysis Spring 2022
Lecturer: Karl-Mikael Perfekt
Messages: The oral exams will be held on 18 and 19 of May. If you intend to take the exam, you must respond to the e-mail that was sent out.
Schedule
From week 12 and onwards, lectures will be held
- Mondays 10.15-12.00 in F2
You are very welcome to visit me in my office in Sentralbygg 2, room 948 on
- Thursdays 11:00-12:00
Office hours are also available at other times, just send me an e-mail.
Teaching material
The course will be based on material from two books:
- Classical and Multilinear Harmonic Analysis, Vol. 1, by C. Muscalu and W. Schlag (M&S)
- Bounded Analytic Functions, by J. B. Garnett (G.)
Both books are available in digital format via the indicated links, if logged into the network of NTNU.
Scope
I aim to cover the following topics:
- Summability and regularity of Fourier series, Marcinkiewicz interpolation (M&S Ch. 1)
- Harmonic functions in the disc and the Hardy—Littlewood maximal function (M&S Ch. 2)
- Conjugate harmonic functions, the Hilbert transform, and the convergence of Fourier series (M&S Ch. 3)
- The theory of Hardy spaces (G. Ch II)
- Bounded Mean Oscillation (G. Ch VI)
Timetable
Lectures will be held on Mondays 10-12 and Thursdays 10-12
| Week | Lectures (Zoom link) | Reading | Exercises | Notes |
|---|---|---|---|---|
| 2 | No lectures this week. Initial meeting Monday 10.01, 13:15 | M&S Ch 1.1-1.3 | See week 3. | |
| 3 | Monday 10-12 (Zoom) and Thursday 10-12 (Zoom) | M&S Ch 1.4-1.6 | Ex: 1.6, 1.9. Prob: 1.1, 1.5, 1.6, 1.7, 1.9 | |
| 4 | Monday 10-12 (room F2) and Thursday 10-12 (room R3) | M&S Ch 2.1-2.4 | Ex: 2.2, 2.4, 2.6, Prob: 2.5, 2.6, 2.7 | |
| 5 | Monday 10-12 (room F2) and Thursday 10-12 (room R3) | M&S Ch 2.5, 3.1-3.2 | Ex 2.8, 2.9, Prob: 2.7, 2.9, 2.10, 3.1, 3.5 | For Problem 3.5, make a Calderon-Zygmund-type decomposition w.r.t. the measure. Use the Besicovitch covering lemma (problem 2.5). |
| 6 | Monday 10-12 (room F2) | M&S Ch. 3.2-3.6 | Ex 3.4, Prob: 3.6, 3.10, 3.12 | No class on Thursday. |
| 7 | Monday 10-12 (room F2) and Thursday 10-12 (room R3) | M&S 3.5-3.6 | Monday is a problem session. | |
| 8 | Monday 10-12 (room F2) and Thursday 10-12 (room R3) | G. II.1-II.5 | ||
| 9 | Monday 10-12 (room F2) and Thursday 10-12 (room R3) | G. II.5 | Ex from G. II: 1, 2(b), 3, 5(a), 5(b), 8 | |
| 10 | Monday 10-12 (room F2) and Thursday 10-12 (room R3) | G. II.6 | ||
| 11 | Monday 10-12 (room F2) and Thursday 10-12 (room R3) | G. II.6-II.7 | ||
| 12 | Monday 10-12 (room F2) | G. I-II | We summarised the theory of harmonic functions and Hardy spaces of the upper half-plane | |
| 13 | Monday 10-12 (room F2) | G. VI.1-VI.2 | ||
| 14 | Monday 10-12 (room F2) | G. VI.2 | ||
| 15 | No lecture | |||
| 16 | Thursday 10-12 (room R3) | G. I.5, VI.3 | We will cover Carleson measures | |
| 17 | Monday 10-12 (room F2) | G. VI. 4 | ||
| 18 | Monday 10-12 (room F2) | Revision | Revision topics |