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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Another characterization of BLO


Author: Colin Bennett
Journal: Proc. Amer. Math. Soc. 85 (1982), 552-556
MSC: Primary 42B25
MathSciNet review: 660603
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Abstract: It is shown that a locally integrable function $ f$ on $ {{\mathbf{R}}^n}$ has bounded lower oscillation $ (f \in {\text{BLO}})$ if and only if $ f = MF + h$, where $ F$ has bounded mean oscillation $ (F \in {\text{BMO}})$ and $ MF < \infty $ a.e., and $ h$ is bounded. Here, $ MF$ is a variant of the familiar Hardy-Littlewood maximal function: $ MF = {\text{sup}_{Q\backepsilon x}}Q(F)$ (no absolute values), where $ Q(F)$ is the mean value of $ F$ over the cube $ Q$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660603-5
PII: S 0002-9939(1982)0660603-5
Article copyright: © Copyright 1982 American Mathematical Society