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A double return times theorem

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Abstract

We prove that for any bounded functions f1, f2 on a measure-preserving dynamical system (X, T) and any distinct integers a1, a2, for almost every x the sequence

$${f_1}\left( {{T^{{a_1}n}}x} \right){f_2}\left( {{T^{{a_2}n}}x} \right)$$

is a good weight for the pointwise ergodic theorem. 1. Introduction

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Pavel Zorin-Kranich

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  1. Pavel Zorin-Kranich
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Correspondence to Pavel Zorin-Kranich.

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Zorin-Kranich, P. A double return times theorem. Isr. J. Math. 229, 255–267 (2019). https://doi.org/10.1007/s11856-018-1797-7

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  • DOI: https://doi.org/10.1007/s11856-018-1797-7

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