整数上的单维离散哈代与雷利希不等式
泛函分析
2024-03-12 v2
摘要
本文考虑形式为的幂权单维离散哈代不等式的加权版本。当为偶数自然数时，我们证明了该不等式并给出最佳常数与余项。我们还在标准与加权雷利希不等式及其高阶版本中找到了显式常数。作为本工作的副产物，我们利用纯分析方法导出了一个组合恒等式。这表明组合恒等式与函数恒等式之间存在关联。
引用
@article{arxiv.2112.10923,
title = {One-dimensional discrete Hardy and Rellich inequalities on integers},
author = {Shubham Gupta},
journal= {arXiv preprint arXiv:2112.10923},
year = {2024}
}
备注
Constant in the Lemma 3.5 corrected. This changed the constants in some of the main theorems; in particular the constant in Corollary 2.4 is 5/16 instead of previous incorrect value of 8/16. Few additional details added and some minor layout changes. This version appears in Journal of Fourier Analysis and Applications