Variable exponent function spaces, Spring 2008

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

• 1.1-1.6; Problem set 1
• 2.1-2.5; Problem set 2
• 4.1, 4.4; Problem set 3
• 7.1, 7.3, 5.1, 7.2; Problem set 4
• 10.1-10.4, 11.4; Problem set 5
• 12.1-3; Problem set 6
• 3.1; 15.3*; There will be no problem set related to these chapters.

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

Schedule

Grade

Prerequisites