Integral Operators in Non-Standard Function Spaces

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

  • Vakhtang Kokilashvili
  • Alexander Meskhi
  • Humberto Rafeiro
  • Stefan Samko

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

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Hölder Spaces of Variable Order

    1. Front Matter
      Pages 569-569
    2. 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
    2. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 607-642
    3. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 643-739
    4. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 741-849
    5. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 851-870
    6. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 871-924
    7. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
      Pages 925-966
  4. Back Matter
    Pages 967-1003

About this book

Introduction

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.

Keywords

Morrey spaces Morrey-Campanato and Herz spaces Sobolev-type theorem commutators compactness grand Bochner spaces grand Lebesgue spaces grand Morrey spaces grand variable exponent Lebesgue spaces maximal, singular and potential operators product kernels variable Herz spaces variable exponent Hölder spaces variable exponent Morrey spaces

Authors and affiliations

  • Vakhtang Kokilashvili
    • 1
  • Alexander Meskhi
    • 2
  • Humberto Rafeiro
    • 3
  • Stefan Samko
    • 4
  1. 1.I. Javakhishvili Tbilisi State UnivTbilisiGeorgia
  2. 2.I. Javakhishvili Tbilisi State UnivTbilisiGeorgia
  3. 3.Pontificia Universidad JaverianaBogotá D.C.Colombia
  4. 4.Departamento de MatemáticaUniversidade do AlgarveFaroPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-21018-6
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-21017-9
  • Online ISBN 978-3-319-21018-6
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site