03824nam a22005535i 4500 978-3-031-64983-7 DE-He213 20251030113233.0 cr nn 008mamaa 241018s2024 sz | s |||| 0|eng d 9783031649837 978-3-031-64983-7 10.1007/978-3-031-64983-7 doi QA329-329.9 PBKF bicssc MAT037000 bisacsh PBKF thema Kokilashvili, Vakhtang. author. aut http://id.loc.gov/vocabulary/relators/aut 86214 Integral Operators in Non-Standard Function Spaces [electronic resource] : Volume 3: Advances in Grand Function Spaces / by Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XIV, 510 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Operator Theory: Advances and Applications, 2296-4878 ; 298 - 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. 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. Operator theory. Functional analysis. Operator Theory. Functional Analysis. Meskhi, Alexander. author. aut http://id.loc.gov/vocabulary/relators/aut 86215 Rafeiro, Humberto. author. aut http://id.loc.gov/vocabulary/relators/aut 41250 Samko, Stefan. author. aut http://id.loc.gov/vocabulary/relators/aut 86216 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031649820 Printed edition: 9783031649844 Printed edition: 9783031649851 Operator Theory: Advances and Applications, 2296-4878 ; 298 74617 https://doi.org/10.1007/978-3-031-64983-7 ZDB-2-SMA ZDB-2-SXMS 64288 64288