Norm-variation of Triple Ergodic Averages for Commuting Transformations

Authors

• Polona Durcik, Chapman UniversityFollow
• Lenka Slavíková, Charles University
• Christoph Thiele, Universität Bonn

Document Type

Article

Publication Date

3-11-2026

Abstract

We prove an r-variation estimate, r>4, in the norm for ergodic averages with respect to three commuting transformations. It is not known whether such estimates hold for all r≥2 as in the analogous cases for one or two commuting transformations, or whether such estimates hold for any r< ∞ for more than three commuting transformations.

Comments

This article was originally published in Analysis & PDE, volume 19, issue 3, in 2026. https://doi.org/10.2140/apde.2026.19.539

Recommended Citation

P. Durcik, L. Slavíková, and C. Thiele, "Norm-variation of triple ergodic averages for commuting transformations", Analysis & PDE 193 (2026), 539–586. https://doi.org/10.2140/apde.2026.19.539

Peer Reviewed

1

Copyright

MSP (Mathematical Sciences Publishers)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.