05203nam 22006734a 450 991045111000332120200520144314.01-281-91924-19786611919245981-277-400-9(CKB)1000000000409735(EBL)1681644(OCoLC)879025571(SSID)ssj0000206777(PQKBManifestationID)11206841(PQKBTitleCode)TC0000206777(PQKBWorkID)10235206(PQKB)10899777(MiAaPQ)EBC1681644(WSP)00006063(Au-PeEL)EBL1681644(CaPaEBR)ebr10201347(CaONFJC)MIL191924(EXLCZ)99100000000040973520060511d2006 uy 0engur|n|---|||||txtccrMultiplicative inequalities of Carlson type and interpolation[electronic resource] /Leo Larsson ... [et al.]New Jersey World Scientificc20061 online resource (217 p.)Description based upon print version of record.981-256-708-9 Includes bibliographical references (p. 193-197) and index.Contents ; 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 Other1. 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 Bellman2.5 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 Beurling3.2 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 Preliminaries5.2 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 Generalizations5.4.1 A Multi-dimensional Extension of Theorem 3.6 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 additionInequalities (Mathematics)InterpolationNumerical analysisElectronic books.Inequalities (Mathematics)Interpolation.Numerical analysis.515/.26Larsson Leo1972-739596MiAaPQMiAaPQMiAaPQBOOK9910451110003321Multiplicative inequalities of Carlson type and interpolation1465121UNINA