Bounded mean oscillation and regulated martingales
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- by Carl Herz PDF
- Trans. Amer. Math. Soc. 193 (1974), 199-215 Request permission
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.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 193 (1974), 199-215
- MSC: Primary 60G45; Secondary 30A78
- DOI: https://doi.org/10.1090/S0002-9947-1974-0353447-5
- MathSciNet review: 0353447