Ornstein’s $L \textrm {log}^{+}L$ theorem
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- by Roger L. Jones PDF
- Proc. Amer. Math. Soc. 91 (1984), 262-264 Request permission
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
- Roger L. Jones, New proofs for the maximal ergodic theorem and the Hardy-Littlewood maximal theorem, Proc. Amer. Math. Soc. 87 (1983), no. 4, 681–684. MR 687641, DOI 10.1090/S0002-9939-1983-0687641-1
- Donald Ornstein, A remark on the Birkhoff ergodic theorem, Illinois J. Math. 15 (1971), 77–79. MR 274719
Additional Information
- © Copyright 1984 American Mathematical Society
- 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