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

ISBN-13: 9781461425472 / Angielski / Miękka / 2012 / 398 str.

Ari Laptev

Opis

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.

Spis treści

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.

Blurb

International Mathematical Series Volume 11
Around the Research of Vladimir Ma'z'ya I
Function Spaces
Edited by Ari Laptev 

Professor Maz'ya is one of the foremost authorities in various fields of functional analysis and partial differential equations. In particular, Maz'ya is a proiminent figure in the development of the theory of Sobolev spaces. He is the author of the well-known monograph Sobolev Spaces (Springer, 1985).

Professor Maz'ya is one of the foremost authorities in various fields of functional analysis and partial differential equations. In particular, Maz'ya is a proiminent figure in the development of the theory of Sobolev spaces. He is the author of the well-known monograph Sobolev Spaces (Springer, 1985). The following topics are discussed in this volume: Orlicz-Sobolev spaces, weighted Sobolev spaces, Besov spaces with negative exponents, Dirichlet spaces and related variational capacities, classical inequalities, including Hardy inequalities (multidimensional versions, the case of fractional Sobolev spaces etc.), Hardy-Maz'ya-Sobolev inequalities, analogs of Maz'ya's isocapacitary inequalities in a measure-metric space setting, Hardy type, Sobolev, Poincare, and pseudo-Poincare inequalities in different contexts including Riemannian manifolds, measure-metric spaces, fractal domains etc., Mazya's capacitary analogue of the coarea inequality in metric probability spaces, sharp constants, extension operators, geometry of hypersurfaces in Carnot groups, Sobolev homeomorphisms, a converse to the Maz'ya inequality for capacities and applications of Maz'ya's capacity method.

Contributors include: Farit Avkhadiev (Russia) and Ari Laptev (UK—Sweden); Sergey Bobkov (USA) and Boguslaw Zegarlinski (UK); Andrea Cianchi (Italy); Martin Costabel (France), Monique Dauge (France), and Serge Nicaise (France); Stathis Filippas (Greece), Achilles Tertikas (Greece), and Jesper Tidblom (Austria); Rupert L. Frank (USA) and Robert Seiringer (USA); Nicola Garofalo (USA-Italy) and Christina Selby (USA); Vladimir Gol'dshtein (Israel) and Aleksandr Ukhlov (Israel); Niels Jacob (UK) and Rene L. Schilling (Germany); Juha Kinnunen (Finland) and Riikka Korte (Finland); Pekka Koskela (Finland), Michele Miranda Jr. (Italy), and Nageswari Shanmugalingam (USA); Moshe Marcus (Israel) and Laurent Veron (France); Joaquim Martin (Spain) and Mario Milman (USA); Eric Mbakop (USA) and Umberto Mosco (USA ); Emanuel Milman (USA); Laurent Saloff-Coste (USA); Jie Xiao (USA)

Ari Laptev -Imperial College London (UK) and Royal Institute of Technology (Sweden). Ari Laptev is a world-recognized specialist in Spectral Theory of Differential Operators. He is the President of the European Mathematical Society for the period 2007- 2010.

Tamara Rozhkovskaya - Sobolev Institute of Mathematics SB RAS (Russia) and an  independent publisher. Editors and Authors are exclusively invited to contribute to volumes highlighting recent advances in various fields of mathematics by the Series Editor and a founder of the IMS Tamara Rozhkovskaya.

Cover image: Vladimir Maz'ya