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arXiv · 1502.01958

Ultracontractivity and functional inequalities on infinite graphs

Yong Lin·Shuang Liu·Hongye Song
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Abstract

In this paper, we prove the equivalent of ultracontractive bound of heat semigroup or the uniform upper bound of the heat kernel with the Nash inequality, Log-Sobolev inequalities on graphs. We also show that under the assumption of volume growth and nonnegative curvature $CDE'(n,0)$ the Sobolev inequality, Nash inequality, Faber-Krahn inequality, Log-Sobolev inequalities, discrete and continuous-time uniform upper estimate of heat kernel are all true on graph.

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Yong Lin, Shuang Liu, Hongye Song. 2015-02-06. Ultracontractivity and functional inequalities on infinite graphs. https://arxiv.org/abs/1502.01958

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