Sharp forms and quantitative stability for general weighted discrete $p$-Hardy inequalities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910098129944576 |
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| author | Yessirkegenov, Nurgissa Zhangirbayev, Amir |
| author_facet | Yessirkegenov, Nurgissa Zhangirbayev, Amir |
| contents | In this paper, we provide a sharp remainder term for the general weighted discrete $p$-Hardy inequality. By simply choosing weights and specifying $1<p<\infty$, we are able to recover the identity by Krej{č}i{ř}{\'ı}k-Štampach [KS22, Theorem 1], obtain the sharp form of the $p$-Hardy inequality by Fischer-Keller-Pogorzelski [FKP23, Theorem 1] and generalize the power weighted inequality by Gupta [Gup22, Theorem 2.1]{gupta2022discrete} with sharp remainder. In addition, we prove a quantitative stability result, thereby showing that any minimizing sequence of the discrete $p$-Hardy inequality must approach the family of non-trivial minimizers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02229 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp forms and quantitative stability for general weighted discrete $p$-Hardy inequalities Yessirkegenov, Nurgissa Zhangirbayev, Amir Functional Analysis 39B62, 26D15 In this paper, we provide a sharp remainder term for the general weighted discrete $p$-Hardy inequality. By simply choosing weights and specifying $1<p<\infty$, we are able to recover the identity by Krej{č}i{ř}{\'ı}k-Štampach [KS22, Theorem 1], obtain the sharp form of the $p$-Hardy inequality by Fischer-Keller-Pogorzelski [FKP23, Theorem 1] and generalize the power weighted inequality by Gupta [Gup22, Theorem 2.1]{gupta2022discrete} with sharp remainder. In addition, we prove a quantitative stability result, thereby showing that any minimizing sequence of the discrete $p$-Hardy inequality must approach the family of non-trivial minimizers. |
| title | Sharp forms and quantitative stability for general weighted discrete $p$-Hardy inequalities |
| topic | Functional Analysis 39B62, 26D15 |
| url | https://arxiv.org/abs/2604.02229 |