Another characterization of BLO
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- by Colin Bennett PDF
- Proc. Amer. Math. Soc. 85 (1982), 552-556 Request permission
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
- Colin Bennett, Ronald A. DeVore, and Robert Sharpley, Weak-$L^{\infty }$ and BMO, Ann. of Math. (2) 113 (1981), no. 3, 601–611. MR 621018, DOI 10.2307/2006999
- R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), no. 2, 249–254. MR 565349, DOI 10.1090/S0002-9939-1980-0565349-8
- Cora Sadosky, Interpolation of operators and singular integrals, Monographs and Textbooks in Pure and Applied Mathematics, vol. 53, Marcel Dekker, Inc., New York, 1979. An introduction to harmonic analysis. MR 551747
Additional Information
- © Copyright 1982 American Mathematical Society
- 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