Around the Research of Vladimir Maz'ya I
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.
New results on actual topics of function spaces presented by leading world-recognized specialists and connected with earlier fundamental results of Prof. Maz'yaThere are several collections of papers honored Prof. Maz'ya. Prof. Maz'ya published more than 20 monographs and more than 450 articles. The range of his interests is very wide and many of his results play a key role in many areas of analysis and PDEs.Nevertheless, the presented volume is absolutely different from all published books honored V. Maz'ya:It focuses on the current state of research in analysis, PDEs and function theory, detailing recent advances, selected in relation to Mazy’as results.All the results are new and never published earlierThe mentioned collections present proceedings of conferences in honor of V. Maz'ya and contributors are participants of these conferences. In this volume contributors and contributions were selected in accordance with the main idea of the volume