Gradient Estimates for the Heat Kernels in Higher Dimensional Heisenberg Groups

摘要

The author obtains sharp gradient estimates for the heat kernels in two kinds of higher dimensional Heisenberg groups—the non-isotropic Heisenberg group and the Heisenberg type group Hn,m. The method used here relies on the positive property of the Bakry-E′mery curvature Γ2 on the radial functions and some associated semigroup technics.