Variable exponent function spaces, Spring 2008

  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


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 domain. Changes in the manuscript are likely, so it is recommended not to print out more than you need at a time.


The course is worth 10 ECTS (5 ov)


Lectures: Mon 12–14, Wed 14–16, starting January 21
There are no separate tutorials for this course


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


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.)