LEADER 03448nam 2200541 450 001 996518465003316 005 20231009151641.0 010 $a3-031-13718-3 024 7 $a10.1007/978-3-031-13718-1 035 $a(MiAaPQ)EBC7209173 035 $a(Au-PeEL)EBL7209173 035 $a(CKB)26191945400041 035 $a(DE-He213)978-3-031-13718-1 035 $a(PPN)269092986 035 $a(EXLCZ)9926191945400041 100 $a20230524d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric harmonic analysis II $efunction spaces measuring size and smoothness on rough sets /$fDorina Mitrea, Irina Mitrea, and Marius Mitrea 205 $a1st ed. 2022. 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2022] 210 4$d©2022 215 $a1 online resource (938 pages) 225 1 $aDevelopments in Mathematics,$x2197-795X ;$v73 311 08$aPrint version: Mitrea, Dorina Geometric Harmonic Analysis II Cham : Springer International Publishing AG,c2023 9783031137174 320 $aIncludes bibliographical references. 327 $a1 Preliminary Functional Analytic Matters -- 2 Abstract Fredholm Theory -- 3 Functions of Vanishing Mean Oscillations and Vanishing Hölder Moduli -- 4 Hardy Spaces on Ahlfors Regular Sets -- 5 Banach Function Spaces, Extrapolation, and Orlicz Spaces -- 6 Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets -- 7 Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets -- 8 Boundary Traces from Weighted Sobolev Spaces into Besov Spaces -- 9 Besov and Triebel-Lizorkin Spaces in Open Sets -- 10 Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morrey Spaces -- 11 Sobolev Spaces on the Geometric Measure Theoretic Boundary of Sets of Locally Finite Perimeter -- A. Terms and Notation Used in Volume II. References -- Index. 330 $aThis monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory. 410 0$aDevelopments in Mathematics,$x2197-795X ;$v73 606 $aMathematics 606 $aAnàlisi harmònica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics. 615 7$aAnàlisi harmònica 676 $a780 700 $aMitrea$b Dorina$0521700 702 $aMitrea$b Irina 702 $aMitrea$b Marius 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996518465003316 996 $aGeometric harmonic analysis II$93371439 997 $aUNISA