Abstract:In this paper, we prove a $p$-Hardy inequality on the discrete half-line with weights $n^{\alpha}$ 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 $\mu$ and $\nu$ 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.
From: Ali Barki [view email]
[v1]
Tue, 31 Dec 2024 06:18:00 UTC (25 KB)
[v2]
Fri, 12 Jun 2026 14:08:57 UTC (24 KB)
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