A note on Sobolev type inequalities on graphs with polynomial volume growth

DOI10.1007/S00013-019-01329-2zbMATH Open1420.05172arXiv1902.02440OpenAlexW2914962936WikidataQ127964133 ScholiaQ127964133MaRDI QIDQ2316823

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Publication date: 7 August 2019

Published in: (Search for Journal in Brave)

Abstract: We prove a scale of generalized $L^p$-Poincar'e inequalities and Sobolev type inequalities on graphs with polynomial volume growth. They are optimal on Vicsek graphs.

Full work available at URL: https://arxiv.org/abs/1902.02440

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Related Items (4)

Instability of the Liouville property for quasi-isometric graphs and manifolds of polynomial volume growth ⋮ Sobolev type inequalities for compact metric graphs ⋮ Riesz means on graphs and discrete groups ⋮ Geometric interpretations of \(L^P\)-Poincaré inequalities on graphs with polynomial volume growth

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