We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors’ recent result obtained for a Euclidean sphere of arbitrary dimension. Furthermore, similar heat kernel bounds are shown in the context of classical Jacobi expansions, on a ball and on a simplex. These results are more precise than the qualitatively sharp Gaussian estimates proved recently by several authors.

中文翻译：

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关于紧致的一阶对称空间，雅可比展开式，球和单形上的真正尖锐的热核估计

我们证明了在所有紧致的秩一对称空间上，对热核的真实的，全球性的双面估计。这概括了作者最近从任意尺寸的欧几里得球体获得的结果。此外，在经典Jacobi展开的背景下，在球上和在单纯形上也显示了相似的热核边界。这些结果比几位作者最近证明的定性的高斯估计更为精确。