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Norm-variation of
triple ergodic averages for commuting transformations
Polona Durcik, Lenka Slavíková and Christoph Thiele |
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Vol. 19 (2026), No. 3, 539–586
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Abstract |
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We prove an -variation estimate, , in the norm for ergodic averages with respect to three commuting transformations. It is not known whether such estimates hold for all as in the analogous cases for one or two commuting transformations, or whether such estimates hold for any for more than three commuting transformations. |
Keywords
ergodic average, multilinear estimate, singular integral
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Mathematical Subject Classification
Primary: 42B20
Secondary: 37A30, 42B15
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Milestones
Received: 30 May 2024
Revised: 7 March 2025
Accepted: 28 April 2025
Published: 11 March 2026
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Authors |
| Polona Durcik | |
| Schmid College of Science and
Technology Chapman University Orange, CA United States |
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| Lenka Slavíková | |
| Department of Mathematical
Analysis Faculty of Mathematics and Physics Charles University Prague Czech Republic |
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| Christoph Thiele | |
| Mathematisches Institut Universität Bonn Bonn Germany |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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