Ruilin Long is Professor at the Institute of Mathematics, Academia Sinica, Peking.
This book gives a systematic introduction to the theory of martingale spaces and inequalities. Except those mainly concerned with the martingale Hp, p>1, most parts of the book reflect the developments in the field in the past twenty years. The material is self-contained, only a familiarity with basic analysis is required. Both graduate students and mathematicians who want to know about the interaction between analysis and probability will find this book to be a valuable reference and text.Das Buch gibt eine systematische Einführung in die Martingaltheorie und ihre Beziehungen zur Analysis. Der größte Teil des Buches beschreibt die Entwicklungen der letzten 20 Jahre.|In the past twenty years, the Hp-BMO Theory on Rn has undergone a flourishing development, which should partly give the credit to the application of some martin gale idea and methods. It would be valuable to exhibit some examples concerning this point. As one of the key parts of Calder6n-Zygmund's real method which first appeared in the 50's, Calder6n-Zygmund Decomposition is exactly the so-called stopping time argument in nature which already existed in the Probability Theory early in the 30's, although such a close relationship between Calder6n-Zygmund De composition and the stopping time argument perhaps was not realized consciously at that time. But after the 70's we actually used the stopping time argument in tentionally as a method of thinking in Analysis. Later, when classical Hp Theory had undergone an evolution from one chapter in the Complex Variable Theory to an independent branch (the key step to accelerate this evolution was D. Burkholder R. Gundy-M. Silverstein's well-known work in the early 70's on the maximal function characterization of Hp), Martingale Hp-BMO Theory soon appeared as a counter part of the classical Hp-BMO Theory. Owing to the simplicity of the structure in martingale setting, many new ideas and methods might be produced easier on this stage. These new things have shown a great effect on the classical Hp-BMO The ory. For example, the concept of atomic decomposition of H P was first germinated in martingale setting; the good >.
Probabilistic Preliminaries - Hp (p>1) Martingales - Inequalities on Martingales - BMO Martingales - Martingale Transforms - Weight Theory and Weighted inequalities - Regular Martingales - Some Applications of Martingale Techniques in Harmonic Analysis.
This book gives a systematic introduction to the theory of martingale spaces and inequalities. Except those mainly concerned with the martingale Hp, p1, most parts of the book reflect the developments in the field in the past twenty years. The material is self-contained, only a familiarity with basic analysis is required. Both graduate students and mathematicians who want to know about the interaction between analysis and probability will find this book to be a valuable reference and text.Das Buch gibt eine systematische Einführung in die Martingaltheorie und ihre Beziehungen zur Analysis. Der größte Teil des Buches beschreibt die Entwicklungen der letzten 20 Jahre.
Probabilistic Preliminaries - Hp (p1) Martingales - Inequalities on Martingales - BMO Martingales - Martingale Transforms - Weight Theory and Weighted inequalities - Regular Martingales - Some Applications of Martingale Techniques in Harmonic Analysis.
Über den Autor
Ruilin Long is Professor at the Institute of Mathematics, Academia Sinica, Peking.
Inhaltsverzeichnis
Probabilistic Preliminaries - Hp (p>1) Martingales - Inequalities on Martingales - BMO Martingales - Martingale Transforms - Weight Theory and Weighted inequalities - Regular Martingales - Some Applications of Martingale Techniques in Harmonic Analysis.
Klappentext
This book gives a systematic introduction to the theory of martingale spaces and inequalities. Except those mainly concerned with the martingale Hp, p>1, most parts of the book reflect the developments in the field in the past twenty years. The material is self-contained, only a familiarity with basic analysis is required. Both graduate students and mathematicians who want to know about the interaction between analysis and probability will find this book to be a valuable reference and text.Das Buch gibt eine systematische Einführung in die Martingaltheorie und ihre Beziehungen zur Analysis. Der größte Teil des Buches beschreibt die Entwicklungen der letzten 20 Jahre.
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