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BMO-boundedness of the maximal operator for arbitrary measures

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Abstract

We show that in the one-dimensional case the weighted Hardy-Littlewood maximal operator M μ is bounded on BMO(μ) for arbitrary Radon measure μ, and that this is not the case in higher dimensions.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 52900, Ramat Gan, Israel

    Andrei K. Lerner

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  1. Andrei K. Lerner
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Lerner, A.K. BMO-boundedness of the maximal operator for arbitrary measures. Isr. J. Math. 159, 243–252 (2007). https://doi.org/10.1007/s11856-007-0045-3

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  • DOI: https://doi.org/10.1007/s11856-007-0045-3

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