Sobolev Spaces in Mathematics I

Chapter 1 My Love Affair with the Sobolev Inequality

Chapter 2 Maximal Functions in Sobolev Spaces

Chapter 3 Hardy Type Inequalities via Riccati and Sturm–Liouville Equations

Chapter 4 Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles

Chapter 5 Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces

Chapter 6 Sobolev Embeddings and Hardy Operators

Chapter 7 Sobolev Mappings between Manifolds and Metric Spaces

Chapter 8 A Collection of Sharp Dilation Invariant Integral Inequalities for Differentiable Functions

Chapter 9 Optimality of Function Spaces in Sobolev Embeddings

Chapter 10 On the Hardy–Sobolev–Maz'ya Inequality and Its Generalizations

Chapter 11 Sobolev Inequalities in Familiar and Unfamiliar Settings

Chapter 13 Cocompact Imbeddings and Structure of Weakly Convergent Sequences