Stability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes

2021 ◽  
pp. 1-26
Keyword(s):  
Heat Kernel ◽  
Jump Processes ◽  
Kernel Estimates ◽  
Heat Kernel Estimates ◽  
Harnack Inequalities

scholarly journals Stability of heat kernel estimates for symmetric non-local Dirichlet forms

2021 ◽  
Vol 271 (1330) ◽  
Author(s):  
Zhen-Qing Chen ◽  
Takashi Kumagai ◽  
Jian Wang
Keyword(s):  
Heat Kernel ◽  
Jump Processes ◽  
Metric Measure Spaces ◽  
Kernel Estimates ◽  
Open Problems ◽  
Content Type ◽  
Heat Kernel Estimates ◽  
Measure Spaces ◽  
Non Local ◽  
Volume Doubling

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, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for α \alpha -stable-like processes even with α ≥ 2 \alpha \ge 2 when the underlying spaces have walk dimensions larger than 2 2 , which has been one of the major open problems in this area.

scholarly journals On the equivalence of parabolic Harnack inequalities and heat kernel estimates

2012 ◽  
Vol 64 (4) ◽  
pp. 1091-1146 ◽  
Author(s):  
Martin T. BARLOW ◽  
Alexander GRIGOR'YAN ◽  
Takashi KUMAGAI
Keyword(s):  
Heat Kernel ◽  
Kernel Estimates ◽  
Heat Kernel Estimates ◽  
Harnack Inequalities
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