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The natural maximal operator on BMO

Author: Winston Ou
Journal: Proc. Amer. Math. Soc. 129 (2001), 2919-2921
MSC (2000): Primary 42B25
Published electronically: February 22, 2001
MathSciNet review: 1840094
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We introduce a generalization of the Hardy-Littlewood maximal operator, the natural maximal operator $M^\natural$, in some sense the maximal operator which most naturally commutes pointwise with the logarithm on $A^\infty$. This commutation reveals the behavior of $M: A^\infty \rightarrow A^1$ to directly correspond to that of $M^\natural: B M O\rightarrow BLO$; the boundedness of $M:B M O \rightarrow BLO$ is an immediate consequence.

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Additional Information

Winston Ou
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637

Received by editor(s): February 3, 2000
Published electronically: February 22, 2001
Additional Notes: The author was partially supported by an NSF Graduate Fellowship. Many thanks to Professor R. Fefferman for his unflagging encouragement and repeated proofreading, and also to Professor C. Kenig for checking over the argument. Any errors are of course the sole property of the author.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2001 American Mathematical Society

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