1. CJM 2013 (vol 66 pp. 641)
||Heat Kernels and Green Functions on Metric Measure Spaces|
We prove that, in a setting of local Dirichlet forms on metric measure
spaces, a two-sided sub-Gaussian estimate of the heat kernel is equivalent
to the conjunction of the volume doubling propety, the elliptic Harnack
inequality and a certain estimate of the capacity between concentric balls.
The main technical tool is the equivalence between the capacity estimate and
the estimate of a mean exit time in a ball, that uses two-sided estimates of
a Green function in a ball.
Keywords:Dirichlet form, heat kernel, Green function, capacity
Categories:35K08, 28A80, 31B05, 35J08, 46E35, 47D07