Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Another characterization of BMO

Authors: R. R. Coifman and R. Rochberg
Journal: Proc. Amer. Math. Soc. 79 (1980), 249-254
MSC: Primary 42B25; Secondary 42B30
MathSciNet review: 565349
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Abstract: The following characterization of functions of bounded mean oscillation (BMO) is proved. f is in BMO if and only if

$\displaystyle f = \alpha \log {g^ \ast } - \beta \log {h^ \ast } + b$

where $ {g^ \ast },({h^ \ast })$ is the Hardy-Littlewood maximal function of g, (h), respectively, b is bounded and $ {\left\Vert f \right\Vert _{{\text{BMO}}}} \leqslant c(\alpha + \beta + {\left\Vert b \right\Vert _\infty })$.

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Article copyright: © Copyright 1980 American Mathematical Society