03473nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001700169072002300186072001600209100008500225245020400310250001800514264007300532300003400605336002600639337002600665338003600691347002400727490006600751505032300817520125501140650002102395650002502416650002102441650002502462700008002487700008002567700007602647710003402723773002602757776003602783776003602819776003602855830006602891856004602957978-3-031-64983-7DE-He21320251030113233.0cr nn 008mamaa241018s2024    sz |    s    |||| 0|eng d  a97830316498377 a10.1007/978-3-031-64983-72doi 4aQA329-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh 7aPBKF2thema1 aKokilashvili, Vakhtang.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aIntegral Operators in Non-Standard Function Spacesh[electronic resource] :bVolume 3: Advances in Grand Function Spaces /cby Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXIV, 510 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aOperator Theory: Advances and Applications,x2296-4878 ;v2980 a- 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.  aThe 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. 0aOperator theory. 0aFunctional analysis.14aOperator Theory.24aFunctional Analysis.1 aMeskhi, Alexander.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aRafeiro, Humberto.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aSamko, Stefan.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303164982008iPrinted edition:z978303164984408iPrinted edition:z9783031649851 0aOperator Theory: Advances and Applications,x2296-4878 ;v29840uhttps://doi.org/10.1007/978-3-031-64983-7