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Sobolev spaces on metric measure spaces

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Author(s): Heinonen J., Koskela P., Shanmugalingam N., Tyson J.T.
Series: New mathematical monographs 27
Publisher: Cambridge University Press
Year: 2015

Language: English
Pages: 448
City: Cambridge

Content: Preface
1. Introduction
2. Review of basic functional analysis
3. Lebesgue theory of Banach space-valued functions
4. Lipschitz functions and embeddings
5. Path integrals and modulus
6. Upper gradients
7. Sobolev spaces
8. Poincare inequalities
9. Consequences of Poincare inequalities
10. Other definitions of Sobolev-type spaces
11. Gromov-Hausdorff convergence and Poincare inequalities
12. Self-improvement of Poincare inequalities
13. An Introduction to Cheeger's differentiation theory
14. Examples, applications and further research directions
References
Notation index
Subject index.