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Around the Research of Vladimir Maz'ya I

Function Spaces

  • Ari Laptev

Part of the International Mathematical Series book series (IMAT, volume 11)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Farit Avkhadiev, Ari Laptev
    Pages 1-12
  3. Martin Costabel, Monique Dauge, Serge Nicaise
    Pages 105-136
  4. Stathis Filippas, Achilles Tertikas, Jesper Tidblom
    Pages 137-160
  5. Rupert L. Frank, Robert Seiringer
    Pages 161-167
  6. Vladimir Gol’dshtein, Alexander Ukhlov
    Pages 207-220
  7. Niels Jacob, René L. Schilling
    Pages 221-238
  8. Juha Kinnunen, Riikka Korte
    Pages 239-254
  9. Pekka Koskela, Michele Miranda Jr., Nageswari Shanmugalingam
    Pages 255-272
  10. Moshe Marcus, Laurent Véron
    Pages 273-284
  11. Joaquim Martín, Mario Milman
    Pages 285-298
  12. Eric Mbakop, Umberto Mosco
    Pages 299-320
  13. Jie Xiao
    Pages 373-390
  14. Back Matter
    Pages 391-395

About this book

Introduction

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

Keywords

Capacity Embeddings Sobolev space Sobolev spaces Sobolev type inequality calculus differential equation distribution linear optimization

Editors and affiliations

  • Ari Laptev
    • 1
  1. 1.Department of MathematicsImperial CollegeLondonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-1341-8
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-1340-1
  • Online ISBN 978-1-4419-1341-8
  • Series Print ISSN 1571-5485
  • Series Online ISSN 1574-8944
  • Buy this book on publisher's site