From Hardy to Rellich inequalities on graphs

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 Schrödinger operators afterwards.

20 pages

Cited by in corpus (5)

• Discrete weighted Hardy Inequality in 1-D
• Hardy and Rellich inequality on lattices
• Improvement of the discrete Hardy inequality
• One-dimensional discrete Hardy and Rellich inequalities on integers
• An optimal fractional Hardy inequality on the discrete half-line