Multiplicative inequalities of Carlson type and interpolation / / Leo Larsson, Lech Maligranda, Josip Pečarić, Lars-Erik Persson

• Autore: Larsson Leo <1972->
• Pubblicazione: Singapore, : World Scientific, 2006
• Descrizione fisica: 1 online resource (217 p.)
• Disciplina: 515/.26
• Soggetto topico: Inequalities (Mathematics); Interpolation; Numerical analysis
• Altri autori: MaligrandaLech PečarićJosip E PerssonLars Erik <1944->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 193-197) and index.
• Nota di contenuto: 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 Other ; 1. 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 ; 2.5 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 ; 3.2 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 ; 5.2 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 ; 5.4.1 A Multi-dimensional Extension of Theorem 3.6
• Sommario/riassunto: 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
• Titolo autorizzato: Multiplicative inequalities of Carlson type and interpolation
• ISBN: 1-281-91924-1; 9786611919245; 981-277-400-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910827975703321
• Lo trovi qui: Univ. Federico II