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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$.


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

  • [1] C. Bennett, R. A. DeVore and R. Sharpley, Weak- $ {L^\infty }$ and BMO, Ann. of Math. (2) 113 (1981), 601-611. MR 621018 (82h:46047)
  • [2] R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), 249-254. MR 565349 (81b:42067)
  • [3] C. Sadosky, Interpolation of operators and singular integrals, Dekker, New York, 1979. MR 551747 (81d:42001)

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

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