变量代换与离散 Hardy 不等式
经典分析与常微分方程
2023-07-12 v1
摘要
对于绝对收敛级数，我们显式给出一个单侧求和估计，可视为半直线上变量代换公式的离散类比。该估计隐含于 Pascal Lefèvre 近期对经典离散 Hardy 不等式的优雅证明中。此处我们去掉了其中多余的不可公度条件，并指出其方法的变量代换特征。这导出了一种更简单、更短且名副其实的 Ingham 型离散 Hardy 不等式证明，并给出了最优常数。
引用
@article{arxiv.2307.04971,
title = {Change of variable and discrete Hardy inequality},
author = {Yi C. Huang},
journal= {arXiv preprint arXiv:2307.04971},
year = {2023}
}
备注
This is a companion note of ''A first order proof of the improved discrete Hardy inequality. Arch. Math. 117, 671-674 (2021)'' and was written in 08/2021. In light of the supersolution language of Pinchover et al., our motivation is to unify, at least conceptually, the proofs for both the discrete and the continuous Hardy inequalities