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arXiv · 2001.05932

Poincar\'e and Hardy inequalities on homogeneous trees

Elvise Berchio·Federico Santagati·Maria Vallarino
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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.

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Elvise Berchio, Federico Santagati, Maria Vallarino. 2020-01-16. Poincar\'e and Hardy inequalities on homogeneous trees. https://doi.org/10.1007/978-3-030-73363-6_1

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