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© 2016

Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

Book

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

  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

  • Book Title Integral Operators in Non-Standard Function Spaces
  • Book Subtitle Volume 1: Variable Exponent Lebesgue and Amalgam Spaces
  • Authors Vakhtang Kokilashvili
    Alexander Meskhi
    Humberto Rafeiro
    Stefan Samko
  • Series Title Operator Theory: Advances and Applications
  • Series Abbreviated Title Operator Theory (Birkhäuser)
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-21014-8
  • Softcover ISBN 978-3-319-79325-2
  • eBook ISBN 978-3-319-21015-5
  • Series ISSN 0255-0156
  • Series E-ISSN 2296-4878
  • Edition Number 1
  • Number of Pages XX, 567
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
    Functional Analysis
  • Buy this book on publisher's site

Reviews

“The book is intended for researchers working in diverse branches of analysis and its applications.” (Boris Rubin, zbMATH 1385.47001, 2018)

“The entire book presents a complete picture of the area in a consecutive way. It could be seen as a short encyclopedia that is very useful as a basis for deeper study but also for further research in the area.” (Nikos Labropoulos, Mathematical Reviews, August, 2017)