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On the weighted integrability of maximal ergodic ratios


Author: Kenneth F. Andersen
Journal: Proc. Amer. Math. Soc. 110 (1990), 319-323
MSC: Primary 28D05
DOI: https://doi.org/10.1090/S0002-9939-1990-1021892-5
MathSciNet review: 1021892
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Abstract: Necessary and sufficient conditions on pairs of nonnegative weight functions are given which ensure that the maximal ergodic ratios defined by means of a measure preserving conservative ergodic transformation satisfy a reverse weak type inequality. From this, weighted integrability results may be deduced.


References [Enhancements On Off] (What's this?)

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  • [2] Y. Derriennic, On the integrability of the supremum of ergodic ratios, Ann. Probab. 1 (1973), 338-340. MR 0352404 (50:4891)
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  • [5] R. Sato, On a reverse maximal ergodic theorem with weights, preprint. MR 722261 (85e:28028)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1021892-5
Keywords: Ergodic ratios, weighted inequalities, reverse weak type inequality, weighted integrability
Article copyright: © Copyright 1990 American Mathematical Society

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