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Integral Operators in Non-Standard Function Spaces

Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces

  • Book
  • © 2016

Overview

Authors:
  1. Vakhtang Kokilashvili

    1. I. Javakhishvili Tbilisi State Univ, Tbilisi, Georgia

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  2. Alexander Meskhi

    1. I. Javakhishvili Tbilisi State Univ, Tbilisi, Georgia

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  3. Humberto Rafeiro

    1. Pontificia Universidad Javeriana, Bogotá D.C., Colombia

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  4. Stefan Samko

    1. Departamento de Matemática, Universidade do Algarve, Faro, Portugal

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  • Presents the first comprehensive account of the two-weight theory of basic integral operators, developed in variable exponent Lebesgue spaces
  • Provides the complete characterizations of Riesz potentials (of functions in variable Lebesgue spaces), weights and space exponents
  • Explores the weak and strong type estimates criteria for fractional and singular integrals
  • Introduces new function spaces that unify variable exponent Lebesgue spaces and grand Lebesgue spaces

Part of the book series: Operator Theory: Advances and Applications (OT, volume 249)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. Hölder Spaces of Variable Order

    1. Front Matter

      Pages 569-569
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    2. Variable Exponent Hölder Spaces

      • Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 571-604

  3. Variable Exponent Morrey–Campanato and Herz Spaces

    1. Front Matter

      Pages 605-605
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    2. Morrey and Stummel Spaces with Constant Exponents

      • Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 607-642

    3. Morrey, Campanato and Herz Spaces with Variable Exponents

      • Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 643-739

    4. Singular Integrals and Potentials in Grand Lebesgue Spaces

      • Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 741-849

    5. Grand Lebesgue Spaces on Sets of Infinite Measure

      • Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 851-870

    6. Fractional and Singular Integrals in Grand Morrey Spaces

      • Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 871-924

    7. Multivariable Operators on the Cone of Decreasing Functions

      • Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 925-966

  4. Back Matter

    Pages 967-1003
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Keywords

About this book

This book, the result of the authors’ long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them.

The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book’s most distinctive features is that the majority of the statements proved here are in the form of criteria.

The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Reviews

“The entire book, which is written in a complete consecutive way of presentation of the material, could be considered as a short encyclopedia, very useful for providing a basis for further research in the area.” (Nikos Labropoulos, Mathematical Reviews, August, 2017)

Authors and Affiliations

  • I. Javakhishvili Tbilisi State Univ, Tbilisi, Georgia

    Vakhtang Kokilashvili, Alexander Meskhi

  • Pontificia Universidad Javeriana, Bogotá D.C., Colombia

    Humberto Rafeiro

  • Departamento de Matemática, Universidade do Algarve, Faro, Portugal

    Stefan Samko

Bibliographic Information

  • Book Title: Integral Operators in Non-Standard Function Spaces

  • Book Subtitle: Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces

  • Authors: Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-319-21018-6

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-21017-9Published: 23 May 2016

  • Softcover ISBN: 978-3-319-79326-9Published: 13 June 2018

  • eBook ISBN: 978-3-319-21018-6Published: 12 May 2016

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XXIII, 434

  • Topics: Operator Theory, Functional Analysis

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