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


Author: Roger L. Jones
Journal: Proc. Amer. Math. Soc. 91 (1984), 262-264
MSC: Primary 28D05
DOI: https://doi.org/10.1090/S0002-9939-1984-0740182-6
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.


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

  • [1] R. L. Jones, New proofs for the maximal ergodic theorem and the Hardy-Littlewood maximal theorem, Proc. Amer. Math. Soc. 87 (1983), 681-684. MR 687641 (84e:28019)
  • [2] D. S. Ornstein, A remark on the Birkhoff ergodic theorem, Illinois J. Math. 15 (1971), 77-79. MR 0274719 (43:479)

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Additional Information

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

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