LEADER 03633nam 22006375 450 001 9910897979903321 005 20260121105200.0 010 $a9783031649837 010 $a3031649834 024 7 $a10.1007/978-3-031-64983-7 035 $a(CKB)36377335300041 035 $a(DE-He213)978-3-031-64983-7 035 $a(MiAaPQ)EBC31732738 035 $a(Au-PeEL)EBL31732738 035 $a(EXLCZ)9936377335300041 100 $a20241018d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntegral Operators in Non-Standard Function Spaces $eVolume 3: Advances in Grand Function Spaces /$fby Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (XIV, 510 p.) 225 1 $aOperator Theory: Advances and Applications,$x2296-4878 ;$v298 311 08$a9783031649820 311 08$a3031649826 320 $aIncludes bibliographical references. 327 $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. 330 $aThe present monograph serves as a natural extension of the prior 2-volume monograph with the same title and by the same authors, which encompassed findings up until 2014. This four-volume project encapsulates the authors? decade-long research in the trending topic of nonstandard function spaces and operator theory. One of the main novelties of the present book is to develop the extrapolation theory, generally speaking, in grand Banach function spaces, and to apply it for obtaining the boundedness of fundamental operators of harmonic analysis, in particular, function spaces such as grand weighted Lebesgue and Lorentz spaces, grand variable exponent Lebesgue/Morrey spaces, mixed normed function spaces, etc. Embeddings in grand variable exponent Haj?asz-Sobolev spaces are also studied. Some applications to the approximation theory and boundary value problems of analytic functions are presented as well. The book is aimed at an audience ranging from researchers in operator theory and harmonic analysis to experts in applied mathematics and post graduate students. In particular, we hope that this book will serve as a source of inspiration for researchers in abstract harmonic analysis, function spaces, PDEs and boundary value problems. 410 0$aOperator Theory: Advances and Applications,$x2296-4878 ;$v298 606 $aOperator theory 606 $aFunctional analysis 606 $aOperator Theory 606 $aFunctional Analysis 606 $aEspais algebraics$2thub 606 $aOperadors integrals$2thub 606 $aVarietats algebraiques$2thub 608 $aLlibres electrònics$2thub 615 0$aOperator theory. 615 0$aFunctional analysis. 615 14$aOperator Theory. 615 24$aFunctional Analysis. 615 7$aEspais algebraics 615 7$aOperadors integrals 615 7$aVarietats algebraiques 676 $a516.35 700 $aKokilashvili$b Vakhtang$060040 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910897979903321 996 $aIntegral Operators in Non-Standard Function Spaces$91983098 997 $aUNINA