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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A mean oscillation inequality


Author: Ivo Klemes
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
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Abstract: It is proved that $ \vert\vert{f^ * }\vert{\vert _{{\text{BMO}}}} \leqslant \vert\vert f\vert{\vert _{{\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 [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] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, 1967.
  • [3] F. Riesz, Sur un théorème de maximum de Mm. Hardy et Littlewood, London Math. Soc. 7 (1932), 10-13.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0774010-0
Article copyright: © Copyright 1985 American Mathematical Society

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