Sharp Weighted Discrete $p$-Hardy Inequality and Stability
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915086946271232 |
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| author | Barki, Ali |
| author_facet | Barki, Ali |
| contents | In this paper, we prove a $p$-Hardy inequality on the discrete half-line with weights $n^α$ for all real $p > 1$. Building on the work of Miclo for $p = 2$ and Muckenhoupt in the continuous settings, we develop a quantitative approach for the existence of a $p$-Hardy inequality involving two measures $μ$ and $ν$ on the discrete half-line. We also investigate the comparison between sharp constants in the discrete and continuous settings and explore the stability of the inequality in the discrete case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp Weighted Discrete $p$-Hardy Inequality and Stability Barki, Ali Functional Analysis Spectral Theory In this paper, we prove a $p$-Hardy inequality on the discrete half-line with weights $n^α$ for all real $p > 1$. Building on the work of Miclo for $p = 2$ and Muckenhoupt in the continuous settings, we develop a quantitative approach for the existence of a $p$-Hardy inequality involving two measures $μ$ and $ν$ on the discrete half-line. We also investigate the comparison between sharp constants in the discrete and continuous settings and explore the stability of the inequality in the discrete case. |
| title | Sharp Weighted Discrete $p$-Hardy Inequality and Stability |
| topic | Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2501.00299 |