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Norm Inequalities for Derivatives and Differences

  • Authors
  • Man Kam Kwong
  • Anton Zettl

Part of the Lecture Notes in Mathematics book series (LNM, volume 1536)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Man Kam Kwong, Anton Zettl
    Pages 1-2
  3. Man Kam Kwong, Anton Zettl
    Pages 3-34
  4. Man Kam Kwong, Anton Zettl
    Pages 35-83
  5. Man Kam Kwong, Anton Zettl
    Pages 84-116
  6. Man Kam Kwong, Anton Zettl
    Pages 117-143
  7. Back Matter
    Pages 144-150

About this book

Introduction

Norm inequalities relating (i) a function and two of its derivatives and (ii) a sequence and two of its differences are studied. Detailed elementary proofs of basic inequalities are given. These are accessible to anyone with a background of advanced calculus and a rudimentary knowledge of the Lp and lp spaces. The classical inequalities associated with the names of Landau, Hadamard, Hardy and Littlewood, Kolmogorov, Schoenberg and Caravetta, etc., are discussed, as well as their discrete analogues and weighted versions. Best constants and the existence and nature of extremals are studied and many open questions raised. An extensive list of references is provided, including some of the vast Soviet literature on this subject.

Keywords

Calc Differential Operators Hadamard Landau Inequality Microsoft Access Norm Inequalities boundary element method calculus derivative differential operator eXist extrema function functions proof

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0090864
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56387-7
  • Online ISBN 978-3-540-47548-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site