Martingale Hardy spaces and their applications in Fourier analysis / Ferenc Weisz.

By: Weisz, Ferenc, 1964-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1568.Publisher: Berlin ; New York : Springer-Verlag, ©1994Description: 1 online resource (viii, 217 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540482956; 3540482954Subject(s): Martingales (Mathematics) | Hardy spaces | Fourier analysis | Martingales (Mathématiques) | Espaces de Hardy | Analyse de Fourier | Fourier analysis | Hardy spaces | Martingales (Mathematics) | Fourier-analyse | Martingalen | Hardy-Raum | Fourier-Transformation | Martingal | Harmonische AnalyseGenre/Form: Electronic books. Additional physical formats: Print version:: Martingale Hardy spaces and their applications in Fourier analysis.DDC classification: 510 s | 519.2/87 LOC classification: QA3 | .L28 no. 1568 | QA274.5Other classification: 31.00 | 31.70 | 31.35 Online resources: Click here to access online
Contents:
Ch. 1. Preliminaries and Notations -- Ch. 2. One-Parameter Martingale Hardy Spaces -- Ch. 3. Two-Parameter Martingale Hardy Spaces -- Ch. 4. Tree Martingales -- Ch. 5. Real Interpolation -- Ch. 6. Inequalities for Vilenkin-Fourier Coefficients.
Action note: digitized 2010 committed to preserveSummary: This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
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Includes bibliographical references (pages 204-213) and index.

This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.

Ch. 1. Preliminaries and Notations -- Ch. 2. One-Parameter Martingale Hardy Spaces -- Ch. 3. Two-Parameter Martingale Hardy Spaces -- Ch. 4. Tree Martingales -- Ch. 5. Real Interpolation -- Ch. 6. Inequalities for Vilenkin-Fourier Coefficients.

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