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Proceedings of the American Mathematical Society
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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0774010-0
PII: S 0002-9939(1985)0774010-0
Article copyright: © Copyright 1985 American Mathematical Society