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Integral Operators in Non-Standard Function Spaces

Volume 3: Advances in Grand Function Spaces

Vakhtang Kokilashvili Alexander Meskhi Humberto Rafeiro Stefan Samko

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English
Birkhauser Verlag AG
18 October 2024
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.
By:   , , ,
Imprint:   Birkhauser Verlag AG
Country of Publication:   Switzerland
Edition:   2024 ed.
Volume:   298
Dimensions:   Height: 235mm,  Width: 155mm, 
ISBN:   9783031649820
ISBN 10:   3031649826
Series:   Operator Theory: Advances and Applications
Pages:   510
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
- 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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