Summability of Multi-Dimensional Fourier Series and Hardy Spaces / Edition 1

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This is the first monograph which considers the theory of more-parameter dyadic and classical Hardy spaces. In this book a new application of martingale and distribution theories is dealt with. The theories of the multi-parameter dyadic martingale and the classical Hardy spaces are applied in Fourier analysis. Several summability methods of d-dimensional trigonometric-, Walsh-, spline-, and Ciesielski-Fourier series and Fourier transforms as well as the d-dimensional dyadic derivative are investigated. The boundedness of the maximal operators of the summations on Hardy spaces, weak (L1, L1) inequalities and a.e. convergence results for the d-dimensional Fourier series are proved.

Audience: This book will be useful for researchers as well as for graduate or postgraduate students whose work involves Fourier analysis, approximations and expansions, sequences, series, summability, probability theory, shastic processes, several complex variables, and analytic spaces.

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Product Details

  • ISBN-13: 9781402005640
  • Publisher: Springer Netherlands
  • Publication date: 3/31/2002
  • Series: Mathematics and Its Applications (closed) Series, #541
  • Edition description: 2002
  • Edition number: 1
  • Pages: 332
  • Product dimensions: 0.88 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface. Acknowledgments. 1. Multi-Dimensional Dyadic Hardy Spaces. 2. Multi-Dimensional Classical Hardy Spaces. 3. Summability of D-Dimensional Walsh-Fourier Series. 4. The D-Dimensional Dyadic Derivative. 5. Summability of D-Dimensional Trigonometric-Fourier Series. 6. Summability of D-Dimensional Fourier Transforms. 7. Spline and Ciesielski Systems. References. Index.

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