## Variable exponent function spaces, Spring 2008

Lecturer

Peter Hästö
This is an advanced course (=syventävä kurssi).
The course is theory laden and especially aimed at Master's level
and graduate students interested in pursuing mathematical research.

March 7th: New version of book available

### Material covered and planned: *=current place

### Content

The course will cover a variety of function spaces, including
Lebesgue, Sobolev, Orlicz, Musielak and variable exponent spaces,
and possibly trace, Triebel-Lizorkin and Besov spaces.
Questions studied in these spaces include density of smooth functions,
Poincaré and Sobolev embeddings, maximal operators, Riesz potentials, etc.
All the above mentioned spaces will be introduced and defined,
but former acquaintance with e.g. Lebesgue spaces is certainly beneficial.
The course sets of at the mathematical stage of about 1930, and
will also cover topics investigated only during the 21st century.

The course is based on the book manuscript

Diening, Harjulehto, Hästö & Ru˛ička,
Variable exponent function spaces

The manuscript can only be opened from within the oulu.fi domain.
Changes in the manuscript are likely, so it is recommended not to print out
more than you need at a time.

### Extent

The course is worth 10 ECTS (5 ov)
### Schedule

Lectures: Mon 12–14, Wed 14–16, starting January 21

There are no separate tutorials for this course
### Grade

There is no exam. The grade is based on solved exercises.
### Prerequisites

Analysis III and at least one of the following courses:
Modern Real Analysis, Harmonic Analysis or Sobolev Spaces
(NB! It is possible to attend the course Modern Real Analysis
concurrently during the Spring term.)