Stability of heat kernel estimates for symmetric jump processes on metric measure spaces
نویسندگان
چکیده
In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, modifications of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for α-stable-like processes even with α ≥ 2 when the underlying spaces have walk dimensions larger than 2, which has been one of the major open problems in this area.
منابع مشابه
Laws of the Iterated Logarithm for Symmetric Jump Processes
Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for β-stable-like processes on α-sets with β > 0.
متن کاملNotes on Heat Kernel Estimates and Parabolic Harnack Inequality for Jump Processes on Metric Measure Spaces
In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality. AMS 2000 Mathematics Subject Classification: Primary 60J75 , 60J35, Secondary 31C25 , 31C05. Running title: Notes on Heat Kernel Estimates and Parabolic Harnack Inequality
متن کاملOn Heat Kernel Estimates and Parabolic Harnack Inequality for Jump Processes on Metric Measure Spaces
In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.
متن کاملGlobal Heat Kernel Estimates for Symmetric Jump Processes
In this paper, we study sharp heat kernel estimates for a large class of symmetric jump-type processes in Rd for all t > 0. A prototype of the processes under consideration are symmetric jump processes on Rd with jumping intensity 1 Φ(|x− y|) Z [α1,α2] c(α, x, y) |x− y|d+α ν(dα), where ν is a probability measure on [α1, α2] ⊂ (0, 2), Φ is an increasing function on [0,∞) with c1e2 β ≤ Φ(r) ≤ c3e...
متن کاملSymmetric Jump Processes and their Heat Kernel Estimates
We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes (or equivalently, a class of symmetric integro-differential operators). We focus on the sharp two-sided estimates for the transition density functions (or heat kernels) of the processes, a priori Hölder estimate and parabolic Harnack inequalities for their parabolic functions....
متن کامل