Estimates of heat kernels for non-local regular Dirichlet forms

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Regularity estimates for elliptic nonlocal operators (2015, background): “em not to be applicable in the general case, though. Related questions on nonlocal Dirichlet forms on metric measure spaces are currently investigated by several groups. We refer to the exposition in [16] for a discussion of results regarding the fundamental solution. 1.7. Notation. Throughout this ”
Stability of heat kernel estimates for symmetric non-local Dirichlet forms (2016, background): “r the assumption that (E,F) is conservative, the Radon measure J(dx,dy) = J(x,y)µ(dx)µ(dy) for some non-negative symmetric function J(x,y), and 3 V(x,r) ≤ crd for some constant d>0, it is shown in [GHL2] that heat kernel upper bound estimate in (1.5) holds if and only if p(t,x,x) ≤ c 1td/α, J(x,y”