Poincaré and Hardy inequalities on homogeneous trees

Abstract

We study Hardy-type inequalities on infinite homogeneous trees. More precisely, we derive optimal Hardy weights for the combinatorial Laplacian in this setting and we obtain, as a consequence, optimal improvements for the Poincaré inequality.

References in corpus (3)

• Stochastic Completeness of Graphs
• Hardy-Poincaré, Rellich and Uncertainty principle inequalities on Riemannian manifolds
• The shifted wave equation on Damek--Ricci spaces and on homogeneous trees

Cited by in corpus (4)

• Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
• Discrete weighted Hardy Inequality in 1-D
• One-dimensional discrete Hardy and Rellich inequalities on integers
• Two-weight dyadic Hardy's inequalities