Sobolev Spaces on Metric Measure Spaces : An Approach Based on Upper Gradients (Hardcover)

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.