One-dimensional discrete Hardy and Rellich inequalities on integers
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910359344906240 |
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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 |