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Integral Operators in Non-Standard Function Spaces: Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces: Operator Theory: Advances and Applications, cartea 249

Autor Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko
en Limba Engleză Hardback – 23 mai 2016
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.
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Specificații

ISBN-13: 9783319210179
ISBN-10: 3319210173
Pagini: 465
Ilustrații: XXIII, 434 p.
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.82 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Operator Theory: Advances and Applications

Locul publicării:Cham, Switzerland

Public țintă

Research

Cuprins

IV: Grand Lebesgue Spaces.- 14 Maximal Functions and Potentials.- 15 Grand Lebesgue Spaces on Sets with Infinite Measure.- V: Grand Morrey Spaces.- 16 Maximal Functions, Fractional and Singular Integrals.- 17 Multiple Operators on the Cone of Decreasing Functions.- A: Grand Bochner Spaces.- Bibliography.- Symbol Index.- Subject Index.IV: Grand Lebesgue Spaces.- 14 Maximal Functions and Potentials.- 15 Grand Lebesgue Spaces on Sets with Infinite Measure.- V: Grand Morrey Spaces.- 16 Maximal Functions, Fractional and Singular Integrals.- 17 Multiple Operators on the Cone of Decreasing Functions.- A: Grand Bochner Spaces.- Bibliography.- Symbol Index.- Subject Index.

Recenzii

“The entire book, which is written in a complete consecutive way of presentation of the material, could be considered as a short encyclopedia, very useful for providing a basis for further research in the area.” (Nikos Labropoulos, Mathematical Reviews, August, 2017)

Textul de pe ultima copertă

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.

Caracteristici

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