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:

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:

  1. Summability and regularity of Fourier series, Marcinkiewicz interpolation (M&S Ch. 1)
  2. Harmonic functions in the disc and the Hardy—Littlewood maximal function (M&S Ch. 2)
  3. Conjugate harmonic functions, the Hilbert transform, and the convergence of Fourier series (M&S Ch. 3)
  4. The theory of Hardy spaces (G. Ch II)
  5. 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
2022-05-02, Karl-Mikael Perfekt