Harmonic Analysis II

Advanced course, University of Helsinki, 2023

In the spring semester of 2023, I taught the course Harmonic Analysis II.

Course description

In this course, we cover topics from the theory of A_p-weights, singular integrals, and Calderón-Zygmund operators.

The course is a continuation of the course Harmonic Analysis I, which covers chapters 1-3 in Juha Kinnunen’s lecture notes on Harmonic Analysis.

Course website

Front page: Link

Moodle (for students): Link


As course material, we mainly used Juha Kinnunen’s lecture notes on Harmonic Analysis, as well as the books Grafakos: Classical Fourier Analysis, Grafakos: Modern Fourier Analysis, Douandikoetxea: Fourier Analysis.

Full playlist of the video lectures (add to youtube.com link): /playlist?list=PLKnTm7UeIVwd9ikpq_lYzyeV6ItEDL7gE

Please see also the table of contents of this playlist for an overview of what topics are covered in each lecture: Link

Essays written by students:

Matrix-valued A_p weights, by Aapo Laukkarinen: Link

Some topics on Carleson Measures, by Zhan Zhang: Link

A short overview on Vinogradov’s Mean Value Theorem and Decoupling Inequalities, by Nirmal Krishnan: Link

Fourier Analysis on LCA groups, by Ville Uotila: Link