Abstract
The pointwise ergodic theorem is proved for prime powers for functions inL p,p>1. This extends a result of Bourgain where he proved a similar theorem forp>(1+√3)/2.
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References
A. Bellow,Perturbation of a sequence, Advances in Math., to appear.
J. Bourgain,On the maximal ergodic theorem for certain subsets of the integers, Isr. J. Math.61 (1988), 39–72.
J. Bourgain,On the pointwise ergodic theorem on L p for arithmetic sets, Isr. J. Math.61 (1988), 73–84.
J. Bourgain,An approach to pointwise ergodic theorems, GAFA-Seminar 1987, Lecture Notes in Math., Springer-Verlag, Berlin, to appear.
A. P. Calderon,Ergodic theory and translation-invariant operators, Proc. Natl. Acad. Sci. U.S.A.59 (1968), 349–353.
G. H. Hardy and E. M. Wright,An Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1971.
G. H. Hardy, J. E. Littlewood and G. Pólya,Inequalities, Cambridge University Press, 1952.
R. C. Vaughan,The Hardy-Littlewood Method, Cambridge University Press, 1981.
A. Zygmund,Trigonometric Series, Cambridge University Press, 1968.
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This paper is a part of the author’s Ph.D. thesis supervised by V. Bergelson.
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Wierdl, M. Pointwise ergodic theorem along the prime numbers. Israel J. Math. 64, 315–336 (1988). https://doi.org/10.1007/BF02882425
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DOI: https://doi.org/10.1007/BF02882425