International Mathematical Series

Around the Research of Vladimir Maz'ya I

Function Spaces

Editors: Laptev, Ari (Ed.)

  • Contains new results on actual topics of function spaces presented by leading specialists and connected with earlier fundamental results of Prof. Maz'ya
  • The volume is totally different from all published books honoring Prof. Maz'ya
  • Focuses on the current state of research in analysis, PDEs and function theory, detailing recent advances
  • All the results are new and have never been published before
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  • ISBN 978-1-4419-1341-8
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  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-1-4419-1340-1
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  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
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  • ISBN 978-1-4614-2547-2
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About this book

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

Table of contents (17 chapters)

  • Hardy Inequalities for Nonconvex Domains

    Avkhadiev, Farit (et al.)

    Pages 1-12

  • Distributions with Slow Tails and Ergodicity of Markov Semigroups in Infinite Dimensions

    Bobkov, Sergey (et al.)

    Pages 13-79

  • On Some Aspects of the Theory of Orlicz–Sobolev Spaces

    Cianchi, Andrea

    Pages 81-104

  • Mellin Analysis of Weighted Sobolev Spaces with Nonhomogeneous Norms on Cones

    Costabel, Martin (et al.)

    Pages 105-136

  • Optimal Hardy—Sobolev—Maz’ya Inequalities with Multiple Interior Singularities

    Filippas, Stathis (et al.)

    Pages 137-160

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4419-1341-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-1-4419-1340-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4614-2547-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Around the Research of Vladimir Maz'ya I
Book Subtitle
Function Spaces
Editors
  • Ari Laptev
Series Title
International Mathematical Series
Series Volume
11
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4419-1341-8
DOI
10.1007/978-1-4419-1341-8
Hardcover ISBN
978-1-4419-1340-1
Softcover ISBN
978-1-4614-2547-2
Series ISSN
1571-5485
Edition Number
1
Number of Pages
XXII, 398
Number of Illustrations and Tables
3 b/w illustrations
Additional Information
Jointly published with Tamara Rozhkovskaya Publisher, Novosibirsk, Russia
Topics