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 249)
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Table of contents (7 chapters)
-
Hölder Spaces of Variable Order
-
Variable Exponent Morrey–Campanato and Herz Spaces
Keywords
- Morrey spaces
- Morrey-Campanato and Herz spaces
- Sobolev-type theorem
- commutators
- compactness
- grand Bochner spaces
- grand Lebesgue spaces
- grand Morrey spaces
- grand variable exponent Lebesgue spaces
- maximal, singular and potential operators
- product kernels
- variable Herz spaces
- variable exponent Hölder spaces
- variable exponent Morrey spaces
About this book
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Integral Operators in Non-Standard Function Spaces
Book Subtitle: Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces
Authors: Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-319-21018-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-21017-9Published: 23 May 2016
Softcover ISBN: 978-3-319-79326-9Published: 13 June 2018
eBook ISBN: 978-3-319-21018-6Published: 12 May 2016
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XXIII, 434
Topics: Operator Theory, Functional Analysis