A mean oscillation inequality
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- by Ivo Klemes PDF
- Proc. Amer. Math. Soc. 93 (1985), 497-500 Request permission
Abstract:
It is proved that $||{f^ * }|{|_{{\text {BMO}}}} \leqslant ||f|{|_{{\text {BMO}}}}$, where ${f^ * }$ is the decreasing rearrangement of a function $f \in {\text {BMO}}([0,1])$. A generalization is given, as well as an example, showing the result fails for the symmetric decreasing rearrangement of a function on the circle.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 G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, 1967. F. Riesz, Sur un théorème de maximum de Mm. Hardy et Littlewood, London Math. Soc. 7 (1932), 10-13.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 497-500
- MSC: Primary 26D15; Secondary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1985-0774010-0
- MathSciNet review: 774010