scholarly journals Weighted Poincaré inequality and heat kernel estimates for finite range jump processes

2008 ◽  
Vol 342 (4) ◽  
pp. 833-883 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Panki Kim ◽  
Takashi Kumagai
Keyword(s):  
Heat Kernel ◽  
Poincaré Inequality ◽  
Jump Processes ◽  
Finite Range ◽  
Kernel Estimates ◽  
Poincare Inequality ◽  
Heat Kernel Estimates ◽  
Weighted Poincaré Inequality

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 Global heat kernel estimates for symmetric jump processes

2011 ◽  
Vol 363 (9) ◽  
pp. 5021-5055 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Panki Kim ◽  
Takashi Kumagai
Keyword(s):  
Heat Kernel ◽  
Jump Processes ◽  
Kernel Estimates ◽  
Heat Kernel Estimates

scholarly journals Heat kernel estimates for symmetric jump processes with mixed polynomial growths

2019 ◽  
Vol 47 (5) ◽  
pp. 2830-2868 ◽  
Author(s):  
Joohak Bae ◽  
Jaehoon Kang ◽  
Panki Kim ◽  
Jaehun Lee
Keyword(s):  
Heat Kernel ◽  
Jump Processes ◽  
Kernel Estimates ◽  
Heat Kernel Estimates

scholarly journals Corrigendum to “Global heat kernel estimates for symmetric jump processes”

2015 ◽  
Vol 367 (10) ◽  
pp. 7515-7515 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Panki Kim ◽  
Takashi Kumagai
Keyword(s):  
Heat Kernel ◽  
Jump Processes ◽  
Kernel Estimates ◽  
Heat Kernel Estimates
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