Function spaces, fall 2008

Lecturer

Mikko Salo

Lectures

Weeks 37-42 and 44-50, Wednesday 14-16 in room B322 and Thursday 14-16 in room B321.

The first lecture is on Wednesday 10th September.

Course description

In mathematical analysis one deals with functions which are differentiable (such as continuously differentiable) or integrable (such as square integrable or L^p). It is often natural to combine the smoothness and integrability requirements, which leads one to introduce various spaces of functions.

This course will give a systematic introduction to those function spaces which are most commonly encountered in analysis. This will include Hölder, Lipschitz, Sobolev, Besov, Triebel-Lizorkin, Hardy, and BMO type spaces. We will try to highlight typical uses of these spaces, and will also give an account of interpolation theory which is an important tool in their study.

The preliminary program for the course is as follows:

1. Sobolev spaces of integer order
2. Interpolation theory
3. Fractional Sobolev spaces, Besov and Triebel-Lizorkin spaces
4. Hardy and BMO spaces

The lectures will be given in English or Finnish, depending on the audience.

Prerequisites

Funktionaalianalyysin peruskurssi, Reaalianalyysi 1

Credits

10 op