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A new proof of a weighted inequality for the ergodic maximal function


Author: Kenneth F. Andersen
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
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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 [Enhancements On Off] (What's this?)

  • [1] E. Atencia and A. de la Torre, A dominated ergodic estimate for $ {L^p}$ spaces with weights, Studia Math. 74 (1982), 35-47. MR 675431 (84f:47005)
  • [2] M. Christ and R. Fefferman, A note on weighted norm inequalities for the Hardy-Littlewood maximal operator, Proc. Amer. Math. Soc. 87 (1983), 447-448. MR 684636 (84g:42017)
  • [3] R. 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)
  • [4] -, Inequalities for the ergodic maximal function, Studia Math. 60 (1977), 111-129. MR 0430208 (55:3215)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0861763-7
Keywords: Maximal functions, ergodic maximal function, weighted inequalities
Article copyright: © Copyright 1986 American Mathematical Society

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