无限图的超压缩性与函数不等式
Ultracontractivity and functional inequalities on infinite graphs
摘要：
本文利用图上的Nash不等式、Log-Sobolev不等式证明了热半群的超压缩界或热核的一致上界的等价性。在体积增长和非负曲率$CDE'(n,0)$的假设下，证明了Sobolev不等式、Nash不等式、Faber-Krahn不等式、Log-Sobolev不等式、热核的离散和连续时间一致上估计在图上都成立.
英文摘要：
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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