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arXiv · 2604.02229

Sharp forms and quantitative stability for general weighted discrete $p$-Hardy inequalities

Nurgissa Yessirkegenov·Amir Zhangirbayev
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Abstract

In this paper, we provide a sharp remainder term for the general weighted discrete $p$-Hardy inequality. By choosing appropriate weights and specifying $1<p<\infty$, we are able to recover the identity by Krej{\v{c}}i{\v{r}}{\'\i}k-\v{S}tampach [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] with a sharp remainder. In addition, we prove a quantitative stability type result, thereby showing that the deficit of the discrete $p$-Hardy inequality controls the weighted distance to the family of non-trivial minimizers.

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Nurgissa Yessirkegenov, Amir Zhangirbayev. 2026-04-02. Sharp forms and quantitative stability for general weighted discrete $p$-Hardy inequalities. https://arxiv.org/abs/2604.02229

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