Poincar\'e and Hardy inequalities on homogeneous trees
Analysis of PDEs
2021-10-14 v1 Functional Analysis
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 Poincar\'e inequality.
Keywords
Cite
@article{arxiv.2001.05932,
title = {Poincar\'e and Hardy inequalities on homogeneous trees},
author = {Elvise Berchio and Federico Santagati and Maria Vallarino},
journal= {arXiv preprint arXiv:2001.05932},
year = {2021}
}