On the Optimality and Decay of p-Hardy Weights on Graphs

2022/12/15 by Florian Fischer, Fischer, Florian · 4 citations
Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2212.07728

Abstract

We construct optimal Hardy weights to subcritical energy functionals h associated with quasilinear Schrödinger operators on locally finite graphs. Here, optimality means that the weight w is the largest possible with respect to a partial ordering, and that the corresponding shifted energy functional h-w is null-critical. Moreover, we show a decay condition of Hardy weights in terms of their integrability with respect to certain integral weights. As an application of the decay condition, we show that null-criticality implies optimality near infinity. We also briefly discuss an uncertainty-type principle and a Rellich-type inequality.

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• Supersolution Construction and Optimal Hardy Inequality for Fractional Laplacians
• Optimal Hardy-weights for the Finsler p-Dirichlet integral with a potential
• Potential Theory and the Boundary of Combinatorial Graphs
• An optimal fractional Hardy inequality on the discrete half-line

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