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arXiv · 1909.02286

From Hardy to Rellich inequalities on graphs

Matthias Keller·Yehuda Pinchover·Felix Pogorzelski
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Abstract

We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schr\"odinger operators afterwards.

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Matthias Keller, Yehuda Pinchover, Felix Pogorzelski. 2019-09-05. From Hardy to Rellich inequalities on graphs. https://doi.org/10.1112/plms.12376

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