The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.

Hardy Inequalities for Nonconvex Domains, F. Avkhadiev, A. Laptev.- Distributions with Slow Tails and Ergodicity of Markov Semigroups in Infinite Dimensions, S. Bobkov, B. Zegarlinski.- On Some Aspects of the Theory of Orlicz-Sobolev Spaces, A. Cianchi.- Mellin Analysis of Weighted Sobolev Spaces with Nonhomogeneous Norms on Cones, M. Costabel et al.- Optimal Hardy-Sobolev-Maz'ya Inequalities with Multiple Interior Singularities, S. Filippas et al.- Sharp Fractional Hardy Inequalities in Half-Spaces, R.L. Frank, R. Seiringer.- Collapsing Riemannian Metrics to Sub-Riemannian and the Geometry of Hypersurfaces in Carnot Groups, N. Garofalo, C. Selby.- Sobolev Homeomorphisms and Composition Operators, V. Gol'dshtein, A. Ukhlov.- Extended Lp Dirichlet Spaces, N. Jacob, R.L. Schilling.- Characterizations for the Hardy Inequality, J. Kinnunen, R. Korte.- Geometric Properties of Planar BV-Extension Domains, P. Koskela et al.- On a New Characterization of Besov Spaces with Negative Exponents, M. Marcus, L. Véron.- Isoperimetric Hardy Type and Poincare Inequalities on Metric Spaces, J. Martin, M. Milman.- Gauge Functions and Sobolev Inequalities on Fluctuating Domains, E. Mbakop, U. Mosco.- A Converse to Maz'ya's Inequality for Capacities under Curvature Lower Bound, E. Milman.- Pseudo-Poincaré Inequalities and Applications to Sobolev Inequalities, L. Saloff-Coste.- The p-Faber-Krahn Inequality Noted, J. Xiao.