Local Nash Inequality and Inhomogeneity of Heat Kernels
Local Nash Inequality and Inhomogeneity of Heat Kernels
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DOI：
10.1112/s0024611504014807
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发表时间：
2004-09
影响因子：
1.8
通讯作者：
Jun Kigami
中科院分区：
文献类型：
--
作者：
Jun Kigami
引入局部纳什不等式作为经典纳什不等式的自然扩展，产生空间均匀的上热核估计。局部纳什不等式包含热核的局部信息，是涉及球体积的空间非齐次热核估计的必要条件，就像 Li 和 Yau 对于具有非负 Ricci 曲率的完全黎曼流形所获得的那样。在体积倍增特性下，局部纳什不等式与退出时间估计相结合，相当于允许空间不均匀性的热核的亚高斯非对角上估计。 2000年数学科目分类60J35、47D07（小学）、28A80、58J35（中学）。
The local Nash inequality is introduced as a natural extension of the classical Nash inequality yielding a space‐homogeneous upper heat kernel estimate. The local Nash inequality contains local information of the heat kernel and is a necessary condition for the space‐inhomogeneous heat kernel estimate involving the volume of balls like the one obtained by Li and Yau for a complete Riemannian manifold with non‐negative Ricci curvature. Under the volume doubling property, the local Nash inequality combined with the exit time estimate is shown to be equivalent to a sub‐Gaussian off‐diagonal upper estimate of the heat kernel allowing space‐inhomogeneity. 2000 Mathematics Subject Classification 60J35, 47D07 (primary), 28A80, 58J35 (secondary).