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Lecture Notes in Mathematics

Lebesgue and Sobolev Spaces with Variable Exponents

Authors: Diening, L., Harjulehto, P., Hästö, P., Ruzicka, M.

  • First book in the area of research
  • Self-contained presentation suitable for both graduate students and researchers
  • Comprehensive book with extensive index and nomenclature
  • Applications for the developed theory is presented in the book
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eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-642-18363-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-18362-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
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About this book

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Reviews

From the reviews:

“The authors provide a comprehensive survey of the state of the art concerning Lebesgue and Sobolev spaces with variable exponents. … The book is also having a rich bibliography of 399 entries, a long list of symbols and an index. It will certainly become a standard reference in this field and stimulate further work in this direction.” (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 165 (1), January, 2012)

“The book is devoted to Lebesgue and Soboley spaces with variable exponents. … The present book consists of the introduction and three parts. … The majority of the results presented in the monograph were obtained by the authors and their collaborators. … the books is a useful source of unified information on Lebesgue and Soboley spaces with variable exponents.” (Alexei Yu. Karlovich, Zentralblatt MATH, Vol. 1222, 2011)

“This book consists of three parts of different lengths and intentions, sub-divided into several chapters. There is a nice figure at the very beginning of the monograph explaining the dependencies among the chapters, together with some recommendations on which parts should be used for first reading or when teaching the subject in a graduate course. … the presentation can thus also be considered as a textbook and extremely useful reference for graduate students and researchers working in related fields … .” (Dorothee D. Haroske, Mathematical Reviews, January, 2013)


Table of contents (14 chapters)

  • Introduction

    Diening, Lars (et al.)

    Pages 1-17

  • A Framework for Function Spaces

    Diening, Lars (et al.)

    Pages 21-68

  • Variable Exponent Lebesgue Spaces

    Diening, Lars (et al.)

    Pages 69-97

  • The Maximal Operator

    Diening, Lars (et al.)

    Pages 99-141

  • The Generalized Muckenhoupt Condition*

    Diening, Lars (et al.)

    Pages 143-197

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-642-18363-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-18362-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lebesgue and Sobolev Spaces with Variable Exponents
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2017
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-18363-8
DOI
10.1007/978-3-642-18363-8
Softcover ISBN
978-3-642-18362-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 509
Number of Illustrations and Tables
10 b/w illustrations
Topics