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

 

Ornstein's $ L\,{\rm log}\sp{+}L$ theorem


Author: Roger L. Jones
Journal: Proc. Amer. Math. Soc. 91 (1984), 262-264
MSC: Primary 28D05
MathSciNet review: 740182
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Abstract: D. S. Ornstein has shown that if the ergodic maximal function of a nonnegative function is in $ {L^1}$ then the function is in $ L{\log ^ + }L$. This paper gives a new simple proof of this fact.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740182-6
PII: S 0002-9939(1984)0740182-6
Keywords: Maximal functions, ergodic maximal function, $ L{\log ^ + }L$
Article copyright: © Copyright 1984 American Mathematical Society