The natural maximal operator on BMO

Ou, Winston

doi:10.1090/S0002-9939-01-05896-8

The natural maximal operator on BMO
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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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