From Hardy to Rellich inequalities on graphs

Autoren: Matthias Keller, Yehuda Pinchover, Felix Pogorzelski (2020)

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 Schrödinger operators afterwards.

Zeitschrift:
Proceedings of the London Mathematical Society
Seiten:
458-477
Band:
122

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