Norm-variation of cubic ergodic averages
arXiv:1903.04370
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.
22 pages; v2: the paper has been rewritten and addresses a gap in the proof from v1