A new proof of a weighted inequality for the ergodic maximal function
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- by Kenneth F. Andersen PDF
- Proc. Amer. Math. Soc. 98 (1986), 619-622 Request permission
Abstract:
E. Atencia and A. de la Torre proved that the ergodic maximal function operator is bounded on ${L^p}(\omega )$ if $\omega$ satisfies an appropriate analogue of Muckenhoupt’s ${A_p}$ condition. An alternate proof of this result is given.References
- E. Atencia and A. de la Torre, A dominated ergodic estimate for $L_{p}$ spaces with weights, Studia Math. 74 (1982), no. 1, 35–47. MR 675431, DOI 10.4064/sm-74-1-35-47
- Michael Christ and Robert Fefferman, A note on weighted norm inequalities for the Hardy-Littlewood maximal operator, Proc. Amer. Math. Soc. 87 (1983), no. 3, 447–448. MR 684636, DOI 10.1090/S0002-9939-1983-0684636-9
- 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
- Roger L. Jones, Inequalities for the ergodic maximal function, Studia Math. 60 (1977), no. 2, 111–129. MR 430208, DOI 10.4064/sm-60-2-111-129
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 619-622
- MSC: Primary 28D05; Secondary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1986-0861763-7
- MathSciNet review: 861763