One-dimensional discrete Hardy and Rellich inequalities on integers

Fuente: arXiv
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Main Author: Gupta, Shubham
Format: Preprint
Published: 2021
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author Gupta, Shubham
author_facet Gupta, Shubham
contents In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights of the form $n^α$. We prove the inequality when $α$ is an even natural number with the sharp constant and remainder terms. We also find explicit constants in standard and weighted Rellich inequalities and its higher order versions. As a by-product of this work we derive a combinatorial identity using purely analytic methods. This suggests a correlation between combinatorial identities and functional identities.
format Preprint
id arxiv_https___arxiv_org_abs_2112_10923
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle One-dimensional discrete Hardy and Rellich inequalities on integers
Gupta, Shubham
Functional Analysis
In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights of the form $n^α$. We prove the inequality when $α$ is an even natural number with the sharp constant and remainder terms. We also find explicit constants in standard and weighted Rellich inequalities and its higher order versions. As a by-product of this work we derive a combinatorial identity using purely analytic methods. This suggests a correlation between combinatorial identities and functional identities.
title One-dimensional discrete Hardy and Rellich inequalities on integers
topic Functional Analysis
url https://arxiv.org/abs/2112.10923