Seminorms for multiple averages along polynomials and applications to joint ergodicity

Exploiting the recent work of Tao and Ziegler on the concatenation theorem on factors, we find explicit characteristic factors for multiple averages along polynomials on systems with commuting transformations, and use them to study criteria of joint ergodicity for sequences of the form ( T 1 p 1 , j...

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Bibliographic Details
Published inJournal d'analyse mathématique (Jerusalem) Vol. 146; no. 1; pp. 1 - 64
Main Authors Donoso, Sebastián, Koutsogiannis, Andreas, Sun, Wenbo
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.08.2022
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Ergodic processes
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
Polynomials
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Summary:Exploiting the recent work of Tao and Ziegler on the concatenation theorem on factors, we find explicit characteristic factors for multiple averages along polynomials on systems with commuting transformations, and use them to study criteria of joint ergodicity for sequences of the form ( T 1 p 1 , j ( n ) ⋯ T d p d , j ( n ) ) n ∈ Z , 1 ≤ j ≤ k , where T 1 , …, T d are commuting measure preserving transformations on a probability measure space and p i, j are integer polynomials. To be more precise, we provide a sufficient condition for such sequences to be jointly ergodic, giving also a characterization for sequences of the form ( T i p ( n ) ) n ∈ Z , 1 ≤ i ≤ d to be jointly ergodic, answering a question due to Bergelson.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-021-0186-z