Vladimir Maz’ya 
Sobolev Spaces in Mathematics I [PDF ebook] 
Sobolev Type Inequalities

My Love Affair with the Sobolev Inequality.- Maximal Functions in Sobolev Spaces.- Hardy Type Inequalities via Riccati and Sturm–Liouville Equations.- Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles.- Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces.- Sobolev Embeddings and Hardy Operators.- Sobolev Mappings between Manifolds and Metric Spaces.- A Collection of Sharp Dilation Invariant Integral Inequalities for Differentiable Functions.- Optimality of Function Spaces in Sobolev Embeddings.- On the Hardy–Sobolev–Maz’ya Inequality and Its Generalizations.- Sobolev Inequalities in Familiar and Unfamiliar Settings.- A Universality Property of Sobolev Spaces in Metric Measure Spaces.- Cocompact Imbeddings and Structure of Weakly Convergent Sequences.