Norm-variation of ergodic averages with respect to two commuting transformations
Dynamical Systems
2019-02-01 v3 Classical Analysis and ODEs
Abstract
We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.
Keywords
Cite
@article{arxiv.1603.00631,
title = {Norm-variation of ergodic averages with respect to two commuting transformations},
author = {Polona Durcik and Vjekoslav Kovač and Kristina Ana Škreb and Christoph Thiele},
journal= {arXiv preprint arXiv:1603.00631},
year = {2019}
}
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28 pages