The natural maximal operator on BMO
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- by Winston Ou PDF
- Proc. Amer. Math. Soc. 129 (2001), 2919-2921 Request permission
Abstract:
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
- Email: wcwou@math.uchicago.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2919-2921
- MSC (2000): Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-01-05896-8
- MathSciNet review: 1840094