Integral Operators in Non-Standard Function Spaces - Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces
Buch | Hardcover
XX, 567 Seiten
2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-21014-8 (ISBN)
139,09 inkl. MwSt

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.

_Preface.- I: Variable Exponent Lebesgue and Amalgam spaces.- 1 Hardy Type Operators.- 2 Oscillating weights.- 3 Kernel Integral Operators.- 4 Two-Weight Estimates.- 5 One-sided Operators.- 6 Two-weight Inequalities for Fractional Maximal Functions.- 7 Hypersingular Integrals.- 8 Description of the Range of Potentials 213.- 9 More on Compactness.- 10 Applications to Singular Integral Equations.- II: Hölder Spaces of Variable Order.- 11 Variable Order Hölder Spaces.- III: Variable Exponent Morrey-Campanato and Herz Spaces.- 12 Morrey Type Spaces; Constant Exponents.- 13 Morrey Type Spaces; Variable Exponents.- Bibliography.- Symbol Index.- Subject Index.

"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)

Erscheint lt. Verlag 20.5.2016
Reihe/Serie Operator Theory: Advances and Applications
Zusatzinfo XX, 567 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte Calderón-Zygmund singular integrals • Compactness • Extrapolation • Fractional integrals • Hardy type operators • Hölder spaces • Hypersingular Integrals • kernel operator • one-sided operators • quasimetric measure spaces • two-weight estimates • variable exponent Lebesgue spaces • weights
ISBN-10 3-319-21014-9 / 3319210149
ISBN-13 978-3-319-21014-8 / 9783319210148
Zustand Neuware
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