首页|The Davies method revisited for heat kernel upper bounds of regular
Dirichlet forms on metric measure spaces
The Davies method revisited for heat kernel upper bounds of regular
Dirichlet forms on metric measure spaces
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
Arxiv
We apply the Davies method to prove that for any regular Dirichlet form on a
metric measure space, an off-diagonal stable-type upper bound of the heat
kernel is equivalent to the conjunction of the on-diagonal upper bound, a
cutoff inequality on any two concentric balls, and the jump kernel upper bound,
for any walk dimension. If in addition the jump kernel vanishes, that is, if
the Dirichlet form is strongly local, we obtain sub-Gaussian upper bound. This
gives a unified approach to obtaining heat kernel upper bounds for both the
non-local and the local Dirichlet forms.
Arxiv
