# Sobolev met Poincaré

### About this Title

**Piotr Hajłasz** and **Pekka Koskela**

Publication: Memoirs of the American Mathematical Society

Publication Year
2000: Volume 145, Number 688

ISBNs: 978-0-8218-2047-6 (print); 978-1-4704-0279-2 (online)

DOI: http://dx.doi.org/10.1090/memo/0688

MathSciNet review: 1683160

MSC (1991): Primary 46E35; Secondary 30C65, 31C25, 53C17, 58J60

### Table of Contents

**Chapters**

- 1. Introduction
- 2. What are Poincaré and Sobolev inequalities?
- 3. Poincaré inequalities, pointwise estimates, and Sobolev classes
- 4. Examples and necessary conditions
- 5. Sobolev type inequalities by means of Riesz potentials
- 6. Trudinger inequality
- 7. A version of the Sobolev embedding theorem on spheres
- 8. Rellich-Kondrachov
- 9. Sobolev classes in John domains
- 10. Poincaré inequality: examples
- 11. Carnot-Carathéodory spaces
- 12. Graphs
- 13. Applications to P.D.E and nonlinear potential theory
- 14. Appendix