THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES

摘要

We apply the Davies method to give a quick proof for the upper estimate of the heat kernel for the non-local Dirichlet form on the ultra-metric space. The key observation is that the heat kernel of the truncated Dirichlet form vanishes when two spatial points are separated by any ball of a radius larger than the truncated range. This new phenomenon arises from the ultra-metric property of the space.