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arXiv · 2106.01058

Decomposition of multicorrelation sequences and joint ergodicity

Sebastián Donoso·Andreu Ferré Moragues·Andreas Koutsogiannis·Wenbo Sun
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Abstract

We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure preserving $\mathbb{Z}^d$-actions with multivariable integer polynomial iterates is the sum of a nilsequence and a null sequence, extending a recent result of the second author. To this end, we develop a new seminorm bound estimate for multiple averages by improving the results in a previous work of the first, third and fourth authors. We also use this approach to obtain new criteria for joint ergodicity of multiple averages with multivariable polynomial iterates on $\mathbb{Z}^{d}$-systems.

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Sebastián Donoso, Andreu Ferré Moragues, Andreas Koutsogiannis, Wenbo Sun. 2021-06-02. Decomposition of multicorrelation sequences and joint ergodicity. https://arxiv.org/abs/2106.01058

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