LEADER 05203nam 22006734a 450 001 9910451110003321 005 20200520144314.0 010 $a1-281-91924-1 010 $a9786611919245 010 $a981-277-400-9 035 $a(CKB)1000000000409735 035 $a(EBL)1681644 035 $a(OCoLC)879025571 035 $a(SSID)ssj0000206777 035 $a(PQKBManifestationID)11206841 035 $a(PQKBTitleCode)TC0000206777 035 $a(PQKBWorkID)10235206 035 $a(PQKB)10899777 035 $a(MiAaPQ)EBC1681644 035 $a(WSP)00006063 035 $a(Au-PeEL)EBL1681644 035 $a(CaPaEBR)ebr10201347 035 $a(CaONFJC)MIL191924 035 $a(EXLCZ)991000000000409735 100 $a20060511d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aMultiplicative inequalities of Carlson type and interpolation$b[electronic resource] /$fLeo Larsson ... [et al.] 210 $aNew Jersey $cWorld Scientific$dc2006 215 $a1 online resource (217 p.) 300 $aDescription based upon print version of record. 311 $a981-256-708-9 320 $aIncludes bibliographical references (p. 193-197) and index. 327 $aContents ; Preface ; 0. Introduction and Notation ; 0.1 Notational Conventions ; 0.1.1 Indices and Exponents ; 0.1.2 Constants ; 0.1.3 Measure Spaces and Related Spaces ; 0.1.4 Interpolation Spaces ; 0.1.5 Linear Mappings Between Normed Spaces ; 0.1.6 Other 327 $a1. Carlson's Inequalities 1.1 Carlson's Proof ; 1.2 Hardy's Proofs ; 1.3 An Alternate Proof ; 1.4 Carlson's Inequality for Finite Sums ; 2. Some Extensions and Complements of Carlson's Inequalities ; 2.1 Gabriel ; 2.2 Levin ; 2.3 Caton ; 2.4 Bellman 327 $a2.5 Two Discrete Carlson By-products 2.6 Landau and Levin-Steckin ; 2.7 Some Extensions of the Landau and Levin-Steckin Inequalities ; 2.7.1 The Case p = 1 ; 2.7.2 General p ; 2.8 Proofs ; 2.9 Levin-Godunova ; 2.10 More About Finite Sums ; 3. The Continuous Case ; 3.1 Beurling 327 $a3.2 Kjellberg 3.3 Bellman ; 3.4 Sz. Nagy ; 3.5 Klefsjo ; 3.6 Hu ; 3.7 Yang-Fang ; 3.8 A Continuous Landau Type Inequality ; 3.9 Integrals on Bounded Intervals ; 4. Levin's Theorem ; 5. Some Multi-dimensional Generalizations and Variations ; 5.1 Some Preliminaries 327 $a5.2 A Sharp Inequality for Cones in Rn 5.3 Some Variations on the Multi-dimensional Theme ; 5.3.1 Kjellberg Revisited ; 5.3.2 Andrianov ; 5.3.3 Pigolkin ; 5.3.4 Bertolo-Fernandez ; 5.3.5 Barza et al ; 5.3.6 Kamaly ; 5.4 Some Further Generalizations 327 $a5.4.1 A Multi-dimensional Extension of Theorem 3.6 330 $a Collecting all the results on the particular types of inequalities, the coverage of this book is unique among textbooks in the literature. The book focuses on the historical development of the Carlson inequalities and their many generalizations and variations. As well as almost all known results concerning these inequalities and all known proof techniques, a number of open questions suitable for further research are considered. Two chapters are devoted to clarifying the close connection between interpolation theory and this type of inequality. Other applications are also included, in addition 606 $aInequalities (Mathematics) 606 $aInterpolation 606 $aNumerical analysis 608 $aElectronic books. 615 0$aInequalities (Mathematics) 615 0$aInterpolation. 615 0$aNumerical analysis. 676 $a515/.26 701 $aLarsson$b Leo$f1972-$0739596 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910451110003321 996 $aMultiplicative inequalities of Carlson type and interpolation$91465121 997 $aUNINA