Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60G45, 30A78

Retrieve articles in all journals with MSC: 60G45, 30A78

Additional Information

Keywords: Martingales, bounded mean oscillation, Hardy class, maximal function, martingale contraction, conjugate function
Article copyright: © Copyright 1974 American Mathematical Society