Integral Operators in Non-Standard Functio...

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2016
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xx 567 S.
ISBN-13:	9783319210148
ISBN-10:	3319210149
Sprache:	Englisch
Herstellernummer:	978-3-319-21014-8
Einband:	Gebunden
Autor:	Kokilashvili, Vakhtang Samko, Stefan Rafeiro, Humberto Meskhi, Alexander
Auflage:	1st edition 2016
Hersteller:	Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 37 mm
Von/Mit:	Vakhtang Kokilashvili (u. a.)
Erscheinungsdatum:	20.05.2016
Gewicht:	1,039 kg