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*Brownian Motion, Hardy Spaces and Bounded Mean Oscillation*# Brownian Motion, Hardy Spaces and Bounded Mean Oscillation

*K. E. Petersen*

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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.

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Year:

1977

Publisher:

Cambridge University Press

Language:

English

Pages:

111

ISBN 10:

0521215129

ISBN 13:

9780521215121

ISBN:

0521215129,9780521215121

Series:

London Mathematical Society Lecture Note Series, 28

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