Lecture "Interpolation spaces" (WS 2019/20)

Lecture "Interpolation spaces" (Winter semester 2019/20)

Prof. Dr. Robert Denk

• Time: Wednesday, 10.00-11.30, in F 426
• The exercise takes place every second week in form of a discussion on the exercise sheets.
• Language: German (English if there are students who don't speak German)

Content:

Is the space L³(Rⁿ) between the spaces L²(Rⁿ) and L⁴(Rⁿ)? And how can one formalize this and obtain information on "intermediate spaces"? The answer is given by the theory of interpolation spaces. In this theory, one can interpolate between two Banach spaces and consider linear operators in these interpolation spaces.

This theory has many applications as, e.g., on Sobolev spaces and Hölder spaces. In this lecture, we will discuss real and complex interpolation, the Theorem of Riesz-Thorin, and different scales of Sobolev spaces.

Pre-requisite for this lecture is knowledge in functional analysis. Basic knowledge in the theory of partial differential equations are of advantage.

Literature:

A list of references can be found the end of the lecture notes.

Lecture notes:

The lecture notes (in German) can be found in ILIAS.

Examination:

The examination takes place in form of an oral examination and can be arranged personally.