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The Blocking Technique, Weighted Mean Operators and Hardy's Inequality

  • Book
  • © 1998

Overview

Authors:
  1. Karl-Goswin Grosse-Erdmann
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1679)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • Karl-Goswin Grosse-Erdmann
    Pages 1-6

  3. The blocking technique

    • Karl-Goswin Grosse-Erdmann
    Pages 7-22

  4. The sequence spaces c(a, p, q) and d(a, p, q)

    • Karl-Goswin Grosse-Erdmann
    Pages 23-47

  5. Applications to matrix operators and inequalities

    • Karl-Goswin Grosse-Erdmann
    Pages 49-76

  6. Integral analogues

    • Karl-Goswin Grosse-Erdmann
    Pages 77-92

  7. Back Matter

    Pages 93-114
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Keywords

About this book

This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.

Bibliographic Information

  • Book Title: The Blocking Technique, Weighted Mean Operators and Hardy's Inequality

  • Authors: Karl-Goswin Grosse-Erdmann

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093486

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-63902-2Published: 19 January 1998

  • eBook ISBN: 978-3-540-69664-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 120

  • Topics: Operator Theory, Real Functions

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