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Convergence and Summability of Fourier Transforms and Hardy Spaces

  • Ferenc Weisz

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. One-Dimensional Hardy Spaces and Fourier Transforms

    1. Front Matter
      Pages 1-1
    2. Ferenc Weisz
      Pages 3-70
    3. Ferenc Weisz
      Pages 71-133
  3. Multi-Dimensional Hardy Spaces and Fourier Transforms

    1. Front Matter
      Pages 135-135
    2. Ferenc Weisz
      Pages 137-202
    3. Ferenc Weisz
      Pages 203-227
  4. Back Matter
    Pages 413-435

About this book

Introduction

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. 
Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.

Keywords

Fejér summability fourier analysis hardy spaces Lebesgue points strong summability harmonic analysis atomic decomposition Hardy-Littlewood maximal function multi-dimensional summability circular, triangular and cubic summability theta-summability

Authors and affiliations

  • Ferenc Weisz
    • 1
  1. 1.Department of Numerical AnalysisEötvös Loránd UniversityBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-56814-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-56813-3
  • Online ISBN 978-3-319-56814-0
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site