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Operator Theory: Advances and Applications

Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

Authors: Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S.

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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
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  • ISBN 978-3-319-21015-5
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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 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)


Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-319-21015-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
Softcover $149.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Integral Operators in Non-Standard Function Spaces
Book Subtitle
Volume 1: Variable Exponent Lebesgue and Amalgam Spaces
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
248
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-21015-5
DOI
10.1007/978-3-319-21015-5
Hardcover ISBN
978-3-319-21014-8
Softcover ISBN
978-3-319-79325-2
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XX, 567
Topics

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