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

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

by Ferenc Weisz, Ferenc Weiz, F. Weisz
     
 

ISBN-10: 1402005644

ISBN-13: 9781402005640

Pub. Date: 03/31/2002

Publisher: Springer Netherlands

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

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Overview

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:
03/31/2002
Series:
Mathematics and Its Applications (closed) Series, #541
Edition description:
2002
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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