Integral Operators in Non-Standard Function Spaces
Volume 1: Variable Exponent Lebesgue and Amalgam Spaces
Authors: Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S.
Free Preview- 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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- About this book
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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
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“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)
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Hardy-type Operators in Variable Exponent Lebesgue Spaces
Pages 1-26
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Maximal, Singular, and Potential Operators in Variable Exponent Lebesgue Spaces with Oscillating Weights
Pages 27-128
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Kernel Integral Operators
Pages 129-217
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Two-weight Estimates
Pages 219-295
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One-sided Operators
Pages 297-354
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Integral Operators in Non-Standard Function Spaces
- Book Subtitle
- Volume 1: Variable Exponent Lebesgue and Amalgam Spaces
- Authors
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- Vakhtang Kokilashvili
- Alexander Meskhi
- Humberto Rafeiro
- Stefan Samko
- 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
