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

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 ker...

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Hlavní autoři: Chen, Zhen-Qing, Kumagai, Takashi, Wang, Jian
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2021
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Dirichlet forms
Dirichlet forms. fast (OCoLC)fst00894618
Kernel functions
Kernel functions. fast (OCoLC)fst00986892
cut-off Sobolev inequality
heat kernel estimate
jumping kernel
Lévy system
metric measure space
Dirichlet form
exit time
Faber-Krahn inequality
Symmetric jump process
stability
capacity
ISBN:9781470448639, 1470448637
ISSN:0065-9266, 1947-6221
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  • Introduction and Main Results -- Preliminaries -- Implications of heat kernel estimates -- Implications of <inline-formula content-type="math/mathml"> C S J ( ϕ ) \mathrm {CSJ}(\phi ) </inline-formula> and <inline-formula content-type="math/mathml"> J ϕ , ≥ \mathrm {J}_{\phi , \geq } </inline-formula> -- Consequences of condition <inline-formula content-type="math/mathml"> J ϕ \mathrm {J}_{\phi } </inline-formula> and mean exit time condition <inline-formula content-type="math/mathml"> E ϕ \mathrm {E}_{\phi } </inline-formula> -- Applications and Examples -- Appendix -- Acknowledgment
  • Cover -- 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 -- Back Cover