Proceedings of the American Mathematical Society

Author(s): Winston Ou
Journal: Proc. Amer. Math. Soc. 129 (2001), 2919-2921.
MSC (2000): Primary 42B25
Posted: February 22, 2001
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B25

Winston Ou
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: wcwou@math.uchicago.edu

DOI: 10.1090/S0002-9939-01-05896-8
PII: S 0002-9939(01)05896-8
Received by editor(s): February 3, 2000
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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