Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro

Integral Operators in Non-Standard Function Spaces

Volume 3: Advances in Grand Function Spaces

• Gebundenes Buch

Produktbeschreibung

The present monograph serves as a natural extension of the prior 2-volume monograph with the same title and by the same authors, which encompassed findings up until 2014. This four-volume project encapsulates the authors' decade-long research in the trending topic of nonstandard function spaces and operator theory.

One of the main novelties of the present book is to develop the extrapolation theory, generally speaking, in grand Banach function spaces, and to apply it for obtaining the boundedness of fundamental operators of harmonic analysis, in particular, function spaces such as grand weighted Lebesgue and Lorentz spaces, grand variable exponent Lebesgue/Morrey spaces, mixed normed function spaces, etc. Embeddings in grand variable exponent Hajlasz-Sobolev spaces are also studied. Some applications to the approximation theory and boundary value problems of analytic functions are presented as well.

The book is aimed at an audience ranging from researchers in operator theory and harmonic analysis to experts in applied mathematics and post graduate students. In particular, we hope that this book will serve as a source of inspiration for researchers in abstract harmonic analysis, function spaces, PDEs and boundary value problems.

Produktdetails

• Operator Theory: Advances and Applications 298
• Verlag: Birkhäuser / Springer Nature Switzerland / Springer, Berlin
• Artikelnr. des Verlages: 978-3-031-64982-0
• Seitenzahl: 524
• Erscheinungstermin: 18. Oktober 2024
• Englisch
• Abmessung: 241mm x 160mm x 34mm
• Gewicht: 889g
• ISBN-13: 9783031649820
• ISBN-10: 3031649826
• Artikelnr.: 70836799

Inhaltsangabe

- 18. Integral Operators on Weighted Grand Lebesgue Spaces (WGLS).- 19. Integral Operators in Grand Mixed-Normed Function Spaces.- 20. Grand Variable Exponent Function Spaces.- 21. Extrapolation in Grand Function Spaces.- 22. Grand Variable Haj lasz-Sobolev and Hölder Spaces.- 23. Grand Lebesgue Type Spaces.

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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.

Rezensionen

"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)