Poincaré and Hardy inequalities on homogeneous trees

Published 16 Jan 2020 in math.AP and math.FA | (2001.05932v1)

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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