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Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

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

Part of the Operator Theory: Advances and Applications book series (OT, volume 248)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 1-26
  3. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 27-128
  4. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 129-217
  5. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 219-295
  6. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 297-354
  7. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 355-394
  8. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 395-438
  9. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 439-454
  10. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 455-465
  11. Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
    Pages 467-528
  12. Back Matter
    Pages 529-567

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

Calderón-Zygmund singular integrals Hardy type operators Hölder spaces compactness extrapolation fractional integrals hypersingular integrals kernel operator one-sided operators quasimetric measure spaces two-weight estimates variable exponent Lebesgue spaces weights

Authors and affiliations

  • Vakhtang Kokilashvili
    • 1
  • Alexander Meskhi
    • 2
  • Humberto Rafeiro
    • 3
  • Stefan Samko
    • 4
  1. 1.A. Razmadze Mathematical InstituteI. Javakhishvili Tbilisi State UnivTbilisiGeorgia
  2. 2.A . Razmadze M athem atical InstituteI. Javakhishvili Tbilisi State UnivTbilisiGeorgia
  3. 3.Pontificia Universidad JaverianaLisboaPortugal
  4. 4.Departamento de MatemáticaUniversidade do AlgarveFaroPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-21015-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-21014-8
  • Online ISBN 978-3-319-21015-5
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site