From Hardy to Rellich inequalities on graphs
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
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.
Topics & Concepts
MathematicsInequalityFunction (biology)Pure mathematicsLaplace operatorWeight functionCombinatoricsMathematical analysisDiscrete mathematicsMaximal functionAdvanced Harmonic Analysis ResearchSpectral Theory in Mathematical PhysicsNonlinear Partial Differential Equations