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arXiv · 2605.25238

Optimal discrete $p$-Hardy-Rellich-Birman inequalities

František Štampach·Jakub Waclawek
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Abstract

We present a theory for constructing optimal lower bounds for the discrete half-line $p$-Laplacian of higher order $\ell\in\mathbb{N}$ and general $p>1$. The abstract framework introduces higher-order monotonicity and asymptotic constraints on a parameter sequence that determines optimal weights. As a concrete application, we specialize the parameter sequence to deduce new optimal discrete $p$-Hardy ($\ell=1$), $p$-Rellich ($\ell=2$), and $p$-Birman ($\ell\geq 3$) inequalities.

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BibTeXRIS

František Štampach, Jakub Waclawek. 2026-05-24. Optimal discrete $p$-Hardy-Rellich-Birman inequalities. https://arxiv.org/abs/2605.25238

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