Abstract
In this paper, we consider subordinate symmetric Markov processes that correspond to non-killing Dirichlet forms enjoying heat kernel estimates on a metric measure space with the volume doubling property. We obtain estimates of the jump kernel of the subordinate process and establish equivalent conditions for the jump kernel following the work of Liu and Murugan (ALEA Lat. Am. J. Probab. Math. Stat. 20(2) (2023), 1271–1281). In particular, we clarify the scale of the jump kernel, which is different from the diffusion type. This result is applicable to non-subordinate processes by the transferring method, which uses the stability of Dirichlet forms.
https://ror.org/00ntfnx83 
