Weighted reverse weak type inequalities for the ergodic maximal function and the classes 𝐿𝑙𝑜𝑔⁺𝐿

Andersen, Kenneth F.; Young, Wo-Sang

doi:10.1090/S0002-9939-1985-0801338-8

Weighted reverse weak type inequalities for the ergodic maximal function and the classes $L\textrm {log}^ +L$
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by Kenneth F. Andersen and Wo-Sang Young PDF

Proc. Amer. Math. Soc. 95 (1985), 275-279 Request permission

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.

References

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B.M.O. and the ergodic maximal function