English

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 d1d\geq 1 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

R2 v1 2026-06-23T08:04:23.713Z