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 Vieweg Monographs 1993; 344 pp; hardcover ISBN-10: 3-528-08397-2 ISBN-13: 978-3-528-08397-7 List Price: US$64 Member Price: US$57.60 Order Code: VW/4 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. A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan. Copublished in cooperation with Peking University Press. Readership Table of Contents Probabilistic preliminaries $$H_p(p\ge 1)$$ martingales $$\Phi$$-inequalities on martingales $$BMO$$ martingales Martingale transforms Weight theory and weighted $$\Phi$$-inequalities Regular martingales Some applications of martingale techniques in harmonic analysis References Symbols Index