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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bounded mean oscillation and regulated martingales


Author: Carl Herz
Journal: Trans. Amer. Math. Soc. 193 (1974), 199-215
MSC: Primary 60G45; Secondary 30A78
MathSciNet review: 0353447
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Abstract: In the martingale context, the dual Banach space to $ {H_1}$ is BMO in analogy with the result of Charles Fefferman [4] for the classical case. This theorem is an easy consequence of decomposition theorems for $ {H_1}$-martingales which involve the notion of $ {L_p}$-regulated $ {L_1}$-martingales where $ 1 < p \leq \infty $. The strongest decomposition theorem is for $ p = \infty $, and this provides full information about BMO. The weaker $ p = 2$ decomposition is fundamental in the theory of martingale transforms.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0353447-5
PII: S 0002-9947(1974)0353447-5
Keywords: Martingales, bounded mean oscillation, Hardy class, maximal function, martingale contraction, conjugate function
Article copyright: © Copyright 1974 American Mathematical Society