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- W4317811193 abstract "Abstract We examine multiple ergodic averages of commuting transformations with polynomial iterates in which the polynomials may be pairwise dependent. In particular, we show that such averages are controlled by the Gowers–Host–Kra seminorms whenever the system satisfies some mild ergodicity assumptions. Combining this result with the general criteria for joint ergodicity established in our earlier work, we determine a necessary and sufficient condition under which such averages are jointly ergodic, in the sense that they converge in the mean to the product of integrals, or weakly jointly ergodic, in that they converge to the product of conditional expectations. As a corollary, we deduce a special case of a conjecture by Donoso, Koutsogiannis, and Sun in a stronger form." @default.
- W4317811193 created "2023-01-24" @default.
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- W4317811193 date "2023-01-23" @default.
- W4317811193 modified "2023-10-14" @default.
- W4317811193 title "Seminorm control for ergodic averages with commuting transformations along pairwise dependent polynomials" @default.
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- W4317811193 doi "https://doi.org/10.1017/etds.2022.117" @default.
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