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

Weighted reverse weak type inequalities for the ergodic maximal function and the classes $ L{\rm log}\sp +L$


Authors: Kenneth F. Andersen and Wo-Sang Young
Journal: Proc. Amer. Math. Soc. 95 (1985), 275-279
MSC: Primary 28D05
MathSciNet review: 801338
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Abstract: D. Ornstein proved that the ergodic maximal function satisfies a reverse weak type inequality, and from this he deduced that the integrability of the maximal function $ {f^ * }$ implies that $ f$ belongs to $ L{\log ^ + }L$. Weighted analogues of these results are proved.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0801338-8
PII: S 0002-9939(1985)0801338-8
Keywords: Maximal functions, ergodic maximal function, weighted inequalities, $ L{\log ^ + }L$
Article copyright: © Copyright 1985 American Mathematical Society