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 Verlag. The AMS is exclusive distributor in North America. Vieweg Verlag 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