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

  • Authors
  • Karl-Goswin Grosse-Erdmann

Part of the Lecture Notes in Mathematics book series (LNM, volume 1679)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Karl-Goswin Grosse-Erdmann
    Pages 1-6
  3. Karl-Goswin Grosse-Erdmann
    Pages 7-22
  4. Karl-Goswin Grosse-Erdmann
    Pages 23-47
  5. Karl-Goswin Grosse-Erdmann
    Pages 49-76
  6. Karl-Goswin Grosse-Erdmann
    Pages 77-92
  7. Back Matter
    Pages 93-114

About this book

Introduction

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.

Keywords

blocking technique classical inequalities function spaces functional analysis operator theory sequence spaces

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093486
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63902-2
  • Online ISBN 978-3-540-69664-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book