Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms.

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Title page
Chapter 1. Introduction and Main Results
1. Setting
2. Heat kernel
Chapter 2. Preliminaries
Chapter 3. Implications of heat kernel estimates
1. \UHK( )+(\sE,\sF) ⟹\J_{ ,≤}, and \HK( )⟹\Jᵩ
2. \UHK( ) (\sE,\sF) ⟹\SCSJ( )
Chapter 4. Implications of \CSJ( ) and \J_{ ,≥}
1. \J_{ ,≥}⟹\FK( )
2. Caccioppoli and ¹-mean value inequalities
3. \FK( )+\J_{ ,≤}+\CSJ( )⟹\Eᵩ
4. \FK( )+\Eᵩ+\J_{ ,≤}⟹\UHKD( )
Chapter 5. Consequences of condition \Jᵩ and mean exit time condition \Eᵩ
1. \UHKD( )+\J_{ ,≤}+\Eᵩ⟹\UHK( ), \Jᵩ+\Eᵩ⟹\UHK( )
2. \Jᵩ+\Eᵩ⟹\LHK( )
Chapter 6. Applications and Examples
1. Applications
2. Counterexample
Chapter 7. Appendix
1. Lévy system formula
2. Meyer's decomposition
3. Some results related to \FK( ).
4. Some results related to (Dirichlet) heat kernel
5. \SCSJ( )+\J_{ ,≤}⟹(\sE,\sF) is conservative
Acknowledgment
Bibliography
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