Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

Integral Operators in Non-Standard Function Spaces (eBook, PDF)

Volume 3: Advances in Grand Function Spaces

• Format: PDF

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 Hajłasz-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

• Verlag: Springer Nature Switzerland
• Seitenzahl: 519
• Erscheinungstermin: 18. Oktober 2024
• Englisch
• ISBN-13: 9783031649837
• Artikelnr.: 71931374

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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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.

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)