Norm-variation of cubic ergodic averages
Dynamical Systems
2025-11-04 v2 Classical Analysis and ODEs
Abstract
We prove a quantitative result on norm convergence of cubic ergodic averages with respect to commuting measure-preserving transformations. We use harmonic analysis techniques, a key tool being estimates for singular Brascamp-Lieb forms with cubical structure, which are used as a black box.
Keywords
Cite
@article{arxiv.1903.04370,
title = {Norm-variation of cubic ergodic averages},
author = {Polona Durcik and Kristina Ana Škreb},
journal= {arXiv preprint arXiv:1903.04370},
year = {2025}
}
Comments
22 pages; v2: the paper has been rewritten and addresses a gap in the proof from v1