Book contents
- Frontmatter
- Dedication
- Contents
- 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 Poincaré inequalities
- 9 Consequences of Poincaré inequalities
- 10 Other definitions of Sobolev-type spaces
- 11 Gromov–Hausdorff convergence and Poincaré inequalities
- 12 Self-improvement of Poincaré inequalities
- 13 An introduction to Cheeger's differentiation theory
- 14 Examples, applications, and further research directions
- References
- Notation index
- Subject index
2 - Review of basic functional analysis
Published online by Cambridge University Press: 05 February 2015
Book contents
- Frontmatter
- Dedication
- Contents
- 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 Poincaré inequalities
- 9 Consequences of Poincaré inequalities
- 10 Other definitions of Sobolev-type spaces
- 11 Gromov–Hausdorff convergence and Poincaré inequalities
- 12 Self-improvement of Poincaré inequalities
- 13 An introduction to Cheeger's differentiation theory
- 14 Examples, applications, and further research directions
- References
- Notation index
- Subject index
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- Sobolev Spaces on Metric Measure SpacesAn Approach Based on Upper Gradients, pp. 7 - 35Publisher: Cambridge University PressPrint publication year: 2015