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Convergence of multiple ergodic averages along polynomials of several variables

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Abstract

LetT be an invertible measure preserving transformation of a probability measure spaceX. Generalizing a recent result of Host and Kra, we prove that the averages\(T^{p1(u)} f\) converge inL 2 (X) for anyf 1 ,…,f r ∃L ∞ (X), any polynomialsp 1 ,…,p r :f 1,...,:f 1∈1\t8(X and and Følner sequence \s{\gF r \s} \t8 r in ℤ d .

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 43210, Columbus, OH, USA

    A. Leibman

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  1. A. Leibman
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Correspondence to A. Leibman.

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Supported by NSF grant DMS-0345350.

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Leibman, A. Convergence of multiple ergodic averages along polynomials of several variables. Isr. J. Math. 146, 303–315 (2005). https://doi.org/10.1007/BF02773538

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  • DOI: https://doi.org/10.1007/BF02773538

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