Quantitative norm convergence of double ergodic averages associated with two commuting group actions (Q2805062)
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scientific article; zbMATH DE number 6578162
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quantitative norm convergence of double ergodic averages associated with two commuting group actions |
scientific article; zbMATH DE number 6578162 |
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Quantitative norm convergence of double ergodic averages associated with two commuting group actions (English)
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9 May 2016
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measure-preserving actions
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\(L^p\) norm-variation estimate
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multiple ergodic averages
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For a pair of commuting measure-preserving actions of the direct sum of countably many copies of a finite abelian group a norm-variational estimate is found for functions in \(L^p\), \(2\leqslant p<\infty\). The strength of the result is that it is quantitative and has certain useful uniformity features. The approach is to use \textit{A. P. Calderón}'s transference principle [Proc. Natl. Acad. Sci. USA 59, 349--353 (1968; Zbl 0185.21806)] to deduce the statement from an estimate for functions on the real line.
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