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.
| Comments: | 30 pages |
| Subjects: | Classical Analysis and ODEs (math.CA); Spectral Theory (math.SP) |
| MSC classes: | 26D15, 39A12, 47J05 |
| Cite as: | arXiv:2605.25238 [math.CA] |
| (or arXiv:2605.25238v1 [math.CA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25238 arXiv-issued DOI via DataCite (pending registration) |
From: František Štampach [view email]
[v1]
Sun, 24 May 2026 19:47:58 UTC (33 KB)
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