Bounded Mean Oscillation and Regulated Martingales

In the martingale context, the dual Banach space to H1is BMO in analogy with the result of Charles Fefferman [4] for the classical case. This theorem is an easy consequence of decomposition theorems for H1-martingales which involve the notion of Lp-regulated L1-martingales where$1 < p \geq \infty...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1974, Vol.193, p.199-215
Main Author: Herz, Carl
Format: Article
Language:English
Subjects:
Banach space
Dyadics
Hilbert spaces
Increasing sequences
Integers
Linear transformations
Martingales
Mathematical functions
Mathematical inequalities
Mathematical theorems
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Summary:In the martingale context, the dual Banach space to H1is BMO in analogy with the result of Charles Fefferman [4] for the classical case. This theorem is an easy consequence of decomposition theorems for H1-martingales which involve the notion of Lp-regulated L1-martingales where$1 < p \geq \infty$. The strongest decomposition theorem is for p = ∞, and this provides full information about BMO. The weaker p = 2 decomposition is fundamental in the theory of martingale transforms.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-1974-0353447-5