Michael Hartz

Hardy Spaces

(Winter term 2019/2020)


Assignment 5 is online.

Time and Place

Lecture (Dec 10 - Feb 7):
Tuesday, 10:15-11:45, SR2
Thursday, 16:00-17:30, SR10

Exercise session: Monday, 10:15-11:45, HS4 (run by Dominik Schillo)

Office Hour: Tuesday, 12:00-13:00, or by appointment


Assignment 1, due December 19.
Assignment 2, due January 9.
Assignment 3, due January 16.
Assignment 4, due January 23.
Assignment 5, due January 30.


Hardy spaces are Banach spaces of holomorphic functions on the unit disc in the complex plane. This topic sits at the interface of complex analysis and functional analysis. On the one hand, Hardy spaces make it possible to study holomorphic functions using tools from functional analysis. On the other hand, they provide a function theoretic approach to questions about operators on Hilbert space. A famous example is Beurling’s theorem, which completely describes all invariant subspaces of the unilateral shift. This course provides an introduction to the theory of Hardy spaces. In particular, the following topics will be covered: Prerequisites are complex analysis (e.g. Funktionentheorie 1) and Lebesgue integration (e.g. Analysis 3). Prior knowledge of functional analysis is helpful, but not required. In particular, this course is suitable for students who are concurrently enrolled in functional analysis.


Main text:
Hoffman, Kenneth, Banach Spaces of Analytic Functions , 2007.

Additional literature:
Duren, Peter L, Theory of Hp Spaces , 2003.
Garnett, John B., Bounded Analytic Functions , 2006.
Koosis, Paul, Introduction to Hp Spaces , 1999.
Nikolski, Nikolai, Hardy Spaces , 2019.

Last update: November 29, 2019   Michael Hartz Impressum