论文标题
关于$ p $ hardy strage的最优性和衰减
On the Optimality and Decay of $p$-Hardy Weights on Graphs
论文作者
论文摘要
我们在本地有限的图表上构建了与Quasilinearschrödinger运算符相关的亚临界能量功能的最佳耐受权重$ h $。在这里，最优性意味着相对于部分订购，权重$ W $是最大的可能性，并且相应移动的能量功能$ H-W $是无效的。此外，我们就某些积分权重的整合性表现出了强耐用权重的衰减条件。作为衰减条件的应用，我们表明无关临界性意味着无穷大附近的最佳性。我们还简要讨论了不确定性型原则和雷利希型不平等。
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.
