LEADER 04281nam 22007095 450 001 9910155299603321 005 20200704092935.0 024 7 $a10.1007/978-3-319-48520-1 035 $a(CKB)3710000000964824 035 $a(DE-He213)978-3-319-48520-1 035 $a(MiAaPQ)EBC4749253 035 $a(PPN)197137695 035 $a(EXLCZ)993710000000964824 100 $a20161128d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis in Banach Spaces $eVolume I: Martingales and Littlewood-Paley Theory /$fby Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XVII, 614 p. 3 illus.) 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v63 311 $a3-319-48519-9 311 $a3-319-48520-2 320 $aIncludes bibliographical references and index. 327 $a1.Bochner Spaces -- 2.Operators on Bochner Spaces -- 3.Martingales -- 4.UMD spaces -- 5. Hilbert transform and Littlewood-Paley Theory -- 6.Open Problems -- A.Mesaure Theory -- B.Banach Spaces -- C.Interpolation Theory -- D.Schatten classes. 330 $aThe present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes.  The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v63 606 $aFourier analysis 606 $aMeasure theory 606 $aPartial differential equations 606 $aProbabilities 606 $aFunctional analysis 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aFourier analysis. 615 0$aMeasure theory. 615 0$aPartial differential equations. 615 0$aProbabilities. 615 0$aFunctional analysis. 615 14$aFourier Analysis. 615 24$aMeasure and Integration. 615 24$aPartial Differential Equations. 615 24$aProbability Theory and Stochastic Processes. 615 24$aFunctional Analysis. 676 $a510 700 $aHytönen$b Tuomas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0748040 702 $avan Neerven$b Jan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVeraar$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWeis$b Lutz$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910155299603321 996 $aAnalysis in Banach Spaces$91989901 997 $aUNINA