Abstract
We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone Vd+1 and its surface V0d+1. To do so, we combine the theory of Jacobi polynomials on the cone explored by Xu with the recent techniques by Nowak, Sjögren, and Szarek, developed to find genuinely sharp estimates for the spherical heat kernel.
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