LEADER 04652nam 22006853 450 001 9910974261603321 005 20250626111448.0 010 $a9781470466381 010 $a1470466384 035 $a(CKB)4940000000609986 035 $a(MiAaPQ)EBC6715036 035 $a(Au-PeEL)EBL6715036 035 $a(RPAM)22487688 035 $a(PPN)258258632 035 $a(OCoLC)1266906499 035 $a(EXLCZ)994940000000609986 100 $a20210901d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$d©2021. 215 $a1 online resource (102 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.271 311 08$a9781470448639 311 08$a1470448637 320 $aIncludes bibliographical references. 327 $aCover -- 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( )?\J? -- 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( )?\E? -- 4. \FK( )+\E?+\J_{ ,?}?\UHKD( ) -- Chapter 5. Consequences of condition \J? and mean exit time condition \E? -- 1. \UHKD( )+\J_{ ,?}+\E??\UHK( ), \J?+\E??\UHK( ) -- 2. \J?+\E??\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. 330 $a"In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for -stable-like processes even with 2 when the underlying spaces have walk dimensions larger than 2, which has been one of the major open problems in this area"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aKernel functions 606 $aProbability theory and stochastic processes -- Markov processes -- Transition functions, generators and resolvents$2msc 606 $aPartial differential equations -- Parabolic equations and systems -- Heat kernel$2msc 606 $aProbability theory and stochastic processes -- Markov processes -- Jump processes$2msc 606 $aPotential theory -- Other generalizations -- Dirichlet spaces$2msc 606 $aProbability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spaces$2msc 606 $aProbability theory and stochastic processes -- Markov processes -- Probabilistic potential theory$2msc 615 0$aKernel functions. 615 7$aProbability theory and stochastic processes -- Markov processes -- Transition functions, generators and resolvents. 615 7$aPartial differential equations -- Parabolic equations and systems -- Heat kernel. 615 7$aProbability theory and stochastic processes -- Markov processes -- Jump processes. 615 7$aPotential theory -- Other generalizations -- Dirichlet spaces. 615 7$aProbability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spaces. 615 7$aProbability theory and stochastic processes -- Markov processes -- Probabilistic potential theory. 676 $a519.2/33 686 $a60J35$a35K08$a60J75$a31C25$a60J25$a60J45$2msc 700 $aChen$b Zhen-Qing$0514801 701 $aKumagai$b Takashi$0525017 701 $aWang$b Jian$f1979-$01829921 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910974261603321 996 $aStability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms$94400060 997 $aUNINA