Martingale Spaces and Inequalities

Inhalt: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.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.Ruilin Long is Professor at the Institute of Mathematics, Academia Sinica, Peking.