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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
DOI: https://doi.org/10.1090/S0002-9939-1982-0660603-5
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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Article copyright: © Copyright 1982 American Mathematical Society