Norm-variation of triple ergodic averages for commuting transformations

Analysis & PDE 2026 Open access

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Authors: Polona Durcik, Lenka Slavíková, Christoph M. Thiele
DOI: 10.2140/apde.2026.19.539
Cited by: 0
References: 20

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.

Fields of Study & Subjects

Limits and Structures in Graph Theory Advanced Harmonic Analysis Research Mathematical Approximation and Integration

Publication details

Journal / source
Analysis & PDE
Volume
19
Issue
3
Pages
539–586
Publication date
11 March 2026
Language
EN