Discrete analogues in harmonic analysis: Multi-parameter Radon averages
Classical Analysis and ODEs
2026-07-20 v1 Dynamical Systems
Abstract
In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method within the framework of Discrete Analogues in Harmonic Analysis. In particular, this gives quantitative estimates for these averages and their underlying Fourier multipliers which reveals an interesting major-arcs rigidity phenomenon. As a consequence, we completely resolve in the affirmative the multi-parameter Bellow--Furstenberg problem in pointwise ergodic theory.
Cite
@article{arxiv.2607.18160,
title = {Discrete analogues in harmonic analysis: Multi-parameter Radon averages},
author = {Agnieszka Hejna-Łyżwa and Joonil Kim and Bartosz Langowski and Mariusz Mirek and Hoyoung Song and James Wright},
journal= {arXiv preprint arXiv:2607.18160},
year = {2026}
}
Comments
72 pages, no figures, dedicated to the memory of Alexandra Bellow (1935-2015)