A conjecture for arithmetic spherical maximal functions
经典分析与常微分方程
2026-05-22 v1
摘要
For 24 years, it has been an open problem to obtain improved bounds, for the maximal function over a sparse sequence of discrete spherical averages, going beyond the range for the full discrete spherical maximal function. I formulate a conjecture to characterize the boundedness of such maximal functions and state a theorem in support of it.
引用
@article{arxiv.2605.22712,
title = {A conjecture for arithmetic spherical maximal functions},
author = {Kevin Hughes},
journal= {arXiv preprint arXiv:2605.22712},
year = {2026}
}
备注
Apologies for not sharing this on the arXiv sooner