Summability of multi-dimensional Fourier series and Hardy spaces /
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 Fourie...
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht ; Boston :
Kluwer Academic,
[2002]
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| Series: | Mathematics and its applications (Kluwer Academic Publishers) ;
volume 541. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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, stochastic processes, several complex variables, and analytic spaces. |
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| Physical Description: | 1 online resource (xv, 332 pages) |
| Bibliography: | Includes bibliographical references (pages 315-330) and index. |
| ISBN: | 9789401731836 (electronic bk.) 9401731837 (electronic bk.) |