scholarly journals A simple approach to functional inequalities for non-local Dirichlet forms

2014 ◽  
Vol 18 ◽  
pp. 503-513 ◽  
Author(s):  
Jian Wang
Keyword(s):  
Dirichlet Forms ◽  
Simple Approach ◽  
Functional Inequalities ◽  
Non Local

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

scholarly journals Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory

2014 ◽  
Vol 266 (8) ◽  
pp. 4765-4808 ◽  
Author(s):  
Rupert L. Frank ◽  
Daniel Lenz ◽  
Daniel Wingert
Keyword(s):  
Spectral Theory ◽  
Dirichlet Forms ◽  
Intrinsic Metrics ◽  
Non Local

scholarly journals Perturbations of functional inequalities for Lévy type Dirichlet forms

2015 ◽  
Vol 27 (6) ◽  
Author(s):  
Xin Chen ◽  
Feng-Yu Wang ◽  
Jian Wang
Keyword(s):  
Diffusion Processes ◽  
Dirichlet Forms ◽  
Functional Inequalities ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Natural Extensions ◽  
Infinite Range

AbstractPerturbations of super Poincaré and weak Poincaré inequalities for Lévy type Dirichlet forms are studied. When the range of jumps is finite, our results are natural extensions to the corresponding ones derived earlier for diffusion processes; and we show that the study for the situation with infinite range of jumps is essentially different. Some examples are presented to illustrate the optimality of our results.

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