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Weighted Hardy Spaces

  • Book
  • © 1989

Overview

Authors:
  1. Jan-Olov Strömberg
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    You can also search for this author in PubMed   Google Scholar

  2. Alberto Torchinsky
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1381)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-V
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  2. Weights

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 1-17

  3. Decomposition of weights

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 18-29

  4. Sharp maximal functions

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 30-47

  5. Functions in the upper half-space

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 48-59

  6. Extensions of distributions

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 60-84

  7. The Hardy spaces

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 85-102

  8. A dense class

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 103-110

  9. The atomic decomposition

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 111-121

  10. The basic inequality

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 122-133

  11. Duality

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 134-149

  12. Singular integrals and multipliers

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 150-176

  13. Complex interpolation

    • Strömberg Jan-Olov, Alberto Torchinsky
    Pages 177-188

  14. Back Matter

    Pages 189-197
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Keywords

About this book

These notes give the basic ingredients of the theory of weighted Hardy spaces of tempered distribution on Rn and illustrate the techniques used. The authors consider properties of weights in a general setting; they derive mean value inequalities for wavelet transforms and introduce halfspace techniques with, for example, nontangential maximal functions and g-functions. This leads to several equivalent definitions of the weighted Hardy space HPW. Fourier multipliers and singular integral operators are applied to the weighted Hardy spaces and complex interpolation is considered. One tool often used here is the atomic decomposition. The methods developed by the authors using the atomic decomposition in the strictly convex case p>1 are of special interest.

Bibliographic Information

  • Book Title: Weighted Hardy Spaces

  • Authors: Jan-Olov Strömberg, Alberto Torchinsky

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0091154

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-51402-2Published: 26 July 1989

  • eBook ISBN: 978-3-540-46207-1Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 200

  • Topics: Geometry

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