Аннотация:
Приведены различные эквавалентные характеризации верхних оценок ядер теплопроводности для регулярных, консервативных и локально Дирихле форм на пространствах с метрикой удвоения, как с аналитической, так и с теоретико-вероятностной точки зрения. В первой части работы используются аналитические соображения, а во второй части основное внимание уделено теоретико-вероятностным аспектам, в которых важную роль играет время выхода.
Статья поступила:16 сентября 2012 г.; исправленный вариант 1 ноября 2013 г.
Liguang Liu, Yuying Zhang, “Fractional Leibniz-type Rules on Spaces of Homogeneous Type”, Potential Anal, 60:2 (2024), 555
Cédric Arhancet, “Spectral triples, Coulhon-Varopoulos dimension and heat kernel estimates”, Advances in Mathematics, 451 (2024), 109794
Bo Li, Bolin Ma, Tianjun Shen, Xiaomei Wu, Chao Zhang, “On the Caloric Functions with BMO Traces and Their Limiting Behaviors”, J Geom Anal, 33:7 (2023)
Daehong KIM, Panki KIM, Kazuhiro KUWAE, “Stability of estimates for fundamental solutions under Feynman–Kac perturbations for symmetric Markov processes”, J. Math. Soc. Japan, 75:2 (2023)
Alexander Grigor'yan, Eryan Hu, Jiaxin Hu, “Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces”, Math. Ann., 2023
Marvin Weidner, “Markov chain approximations for nonsymmetric processes”, Stochastic Processes and their Applications, 158 (2023), 238
Zhen-Qing Chen, Panki Kim, Takashi Kumagai, Jian Wang, Springer Proceedings in Mathematics & Statistics, 394, Dirichlet Forms and Related Topics, 2022, 63
Jiaxin Hu, Guanhua Liu, “Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces”, Forum Mathematicum, 34:1 (2022), 225
Mathias Braun, “Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel”, Journal of Functional Analysis, 283:7 (2022), 109599
Zhen-Qing Chen, Panki Kim, Takashi Kumagai, Jian Wang, “Heat kernels for reflected diffusions with jumps on inner uniform domains”, Trans. Amer. Math. Soc., 375:10 (2022), 6797
Tianjun Shen, Bo Li, “Schrödinger Harmonic Functions with Morrey Traces on Dirichlet Metric Measure Spaces”, Mathematics, 10:7 (2022), 1112
Chen Zh.-Q., Kumagai T., Wang J., “Stability of Heat Kernel Estimates For Symmetric Non-Local Dirichlet Forms”, Mem. Am. Math. Soc., 271:1330 (2021), 1+
Chen Zh.-Q., Kim P., Kumagai T., Wang J., “Heat Kernel Upper Bounds For Symmetric Markov Semigroups”, J. Funct. Anal., 281:4 (2021), 109074
Cao J., Grigor'yan A., Liu L., “Hardy'S Inequality and Green Function on Metric Measure Spaces”, J. Funct. Anal., 281:3 (2021), 109020
Bendikov A., Grigor'yan A., Hu E., Hu J., “Heat Kernels and Non-Local Dirichlet Forms on Ultrametric Spaces”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 22:1 (2021), 399–461
Zhen-Qing Chen, Takashi Kumagai, Jian Wang, “Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms”, Advances in Mathematics, 374 (2020), 107269
Anup Biswas, Janna Lierl, “Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces”, Journal of Functional Analysis, 278:8 (2020), 108429
Janna Lierl, “Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet forms”, Journal de Mathématiques Pures et Appliquées, 140 (2020), 1
Sheng-Hui Chen, Jian Wang, “Characterizations of heat kernel estimates for symmetric non-local Dirichlet forms via resistance forms”, Tohoku Math. J. (2), 72:4 (2020)
P. Horn, Y. Lin, Sh. Liu, Sh.-T. Yau, “Volume doubling, Poincare inequality and Gaussian heat kernel estimate for non-negatively curved graphs”, J. Reine Angew. Math., 757 (2019), 89–130
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