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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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