A remark on $A_ 1$-weights for the strong maximal function
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- by Fernando Soria PDF
- Proc. Amer. Math. Soc. 100 (1987), 46-48 Request permission
Abstract:
If $g$ is a locally integrable function and $M$ is the Hardy-Littlewood maximal function then ${(Mg)^\delta }$ represents an ${A_1}$-weight of $M$ for every $0 < \delta < 1$; that is, $M{(Mg)^\delta }(x) \leq {C_\delta }{(Mg(x))^\delta }$ a.e. In this paper we show that this result does not hold in general if we replace $M$ by the strong maximal operator.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 46-48
- MSC: Primary 42B20; Secondary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883399-5
- MathSciNet review: 883399