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Brownian Motion, Hardy Spaces and Bounded Mean Oscillation

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This exposition of research on the martingale and analytic inequalities associated with Hardy spaces and functions of bounded mean oscillation (BMO) introduces the subject by concentrating on the connection between the probabilistic and analytic approaches. Short surveys of classical results on the maximal, square and Littlewood-Paley functions and the theory of Brownian motion introduce a detailed discussion of the Burkholder-Gundy-Silverstein characterization of HP in terms of maximal functions. The book examines the basis of the abstract martingale definitions of HP and BMO, makes generally available for the first time work of Gundy et al. on characterizations of BMO, and includes a probabilistic proof of the Fefferman-Stein Theorem on the duality of H11 and BMO.

Author(s): K. E. Petersen
Series: London Mathematical Society Lecture Note Series, 28
Publisher: Cambridge University Press
Year: 1977

Language: English
Pages: 111
City: Cambridge

Contents
Preface
1. Introduction
2. The maximal, square and Littlewood-Paley functions
3. Brownian motion
4. Distribution equivalence of the two maximal functions
5. Inequalities for the conjugate function
6. The maximal function characterization of HP
7. The martingale versions of HP and BMO
References
Index