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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on $ A\sb 1$-weights for the strong maximal function


Author: Fernando Soria
Journal: Proc. Amer. Math. Soc. 100 (1987), 46-48
MSC: Primary 42B20; Secondary 42B25
MathSciNet review: 883399
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0883399-5
PII: S 0002-9939(1987)0883399-5
Keywords: Maximal operators, weights, product domains
Article copyright: © Copyright 1987 American Mathematical Society