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On the ergodic Hilbert transform for Lamperti operators


Author: Ryotaro Sato
Journal: Proc. Amer. Math. Soc. 99 (1987), 484-488
MSC: Primary 47A35; Secondary 44A15
DOI: https://doi.org/10.1090/S0002-9939-1987-0875385-6
MathSciNet review: 875385
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Abstract: This paper is devoted to the proof of almost everywhere existence of the ergodic Hilbert transform for a class of Lamperti operators.


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  • [1] P. Billingsley, Ergodic theory and information, Wiley, New York, 1965. MR 0192027 (33:254)
  • [2] A. P. Calderón, Ergodic theory and translation-invariant operators, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 349-353. MR 0227354 (37:2939)
  • [3] M. Cotlar, A unified theory of Hilbert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105-167. MR 0084632 (18:893d)
  • [4] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Interscience, New York, 1958. MR 0117523 (22:8302)
  • [5] P. R. Halmos, Measure theory, Van Nostrand, New York, 1950. MR 0033869 (11:504d)
  • [6] R. Hunt, B. Muckenhoupt, and R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251. MR 0312139 (47:701)
  • [7] A. Ionescu Tulcea, Ergodic properties of isometries in $ {L^p}$ spaces, $ 1 < p < \infty $, Bull. Amer. Math. Soc. 70 (1964), 366-371. MR 0206207 (34:6026)
  • [8] C. H. Kan, Ergodic properties of Lamperti operators, Canad. J. Math. 30 (1978), 1206-1214. MR 511557 (80g:47037)
  • [9] J. Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459-466. MR 0105017 (21:3764)
  • [10] K. Petersen, Another proof of the existence of the ergodic Hilbert transform, Proc. Amer. Math. Soc. 88 (1983), 39-43. MR 691275 (84i:28022)
  • [11] R. Sato, On the ergodic Hilbert transform for operators in $ {L_p},1 < p < \infty $ (submitted).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0875385-6
Keywords: Ergodic Hilbert transform, Lamperti operators, $ {L_p}$ isometries, measure preserving transformations
Article copyright: © Copyright 1987 American Mathematical Society

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