Overview
- 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
Part of the book series: Operator Theory: Advances and Applications (OT, volume 248)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (10 chapters)
-
Front Matter
-
Back Matter
Keywords
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 mathematicsand prospective students.
Reviews
“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)
Authors and Affiliations
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
DOI: https://doi.org/10.1007/978-3-319-21015-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-21014-8Published: 20 May 2016
Softcover ISBN: 978-3-319-79325-2Published: 26 May 2018
eBook ISBN: 978-3-319-21015-5Published: 11 May 2016
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XX, 567
Topics: Operator Theory, Functional Analysis