Around the Research of Vladimir Maz'ya I: Function Spaces [Hardcover]

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.

The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known. This volume contains new results on actual topics of function spaces presented by leading and world-renowned specialists.

Professor Maz'ya - one of the main developers of the modern theory of Sobolev spaces - contributed to the theory in many various directions. The strong influence of his fundamental works is traced in recent results presented in this volume from world-recognized specialists. The topics cover various aspects of the theory of function spaces, including Orlicz-Sobolev spaces, weighted Sobolev spaces, Dirichlet spaces, Besov Spaces with negative exponents, fractional Sobolev spaces on half-spaces and sharp constants in the Hardy inequality, Maz'ya's capacitary analogue of the co-area inequality adapted to the setting of metric probability spaces, Hardy-Sobolev-Maz'ya inequalities, converse of Maz'ya's inequality for capacities, Hersch's isoperimetric inequality, isoperimetric Hardy type and Poincare inequalities on metric spaces, isoperimetric problems in connection with Carnot groups, pseudo-Poincare inequalities and applications to Sobolev inequalities, Sobolev inequalities on fluctuating domains, Sobolev homeomorphisms and composition operators, extension domains for functions with bounded variation.