Integral Operators in Non-Standard Function Spaces: Volume 1: Variable Exponent Lebesgue and Amalgam Spaces: 248 (Operator Theory: Advances and Applications) - Hardcover

Kokilashvili, Vakhtang; Meskhi, Alexander; Rafeiro, Humberto

Hardcover

ISBN 10: 3319210149 ISBN 13: 9783319210148

Verlag: Birkhäuser, 2016

Inhaltsangabe

<P>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.</P><P>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.</P><P>THE BOOK IS INTENDED FOR A BROAD AUDIENCE, RANGING FROM RESEARCHERS IN THE AREA TO EXPERTS IN APPLIED MATHEMATICS AND PROSPECTIVE STUDENTS.</P>

Über diesen Titel

Críticas

“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)

Reseña del editor

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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2016
• ISBN 10: 3319210149
• ISBN 13: 9783319210148
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 1
• Anzahl der Seiten: 588