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arXiv · 2608.30551

Critical discrete Hardy inequalities in $L^p$

Krzysztof Bogdan·Shubham Gupta·Kamil Kaleta·Antoni Szczukiewicz
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Abstract

We establish ground-state representations and critical Hardy inequalities in the discrete $L^p$ setting. In particular, we construct critical Hardy weights for the discrete Dirichlet Laplacian on the half-line and the discrete fractional Laplacian on the integers for all $p\in(1,\infty)$. Our approach uses Sobolev--Bregman forms, for which the ground-state representations are exact identities and the corresponding Hardy weights are expressed through linear operators acting on powers of positive superharmonic functions.

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Krzysztof Bogdan, Shubham Gupta, Kamil Kaleta, Antoni Szczukiewicz. 2026-08-31. Critical discrete Hardy inequalities in $L^p$. https://arxiv.org/abs/2608.30551

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