Heat kernel estimates for jump processes of mixed types on metric measure spaces

DOI10.1007/s00440-007-0070-5zbMath1131.60076OpenAlexW2000988163MaRDI QIDQ2464676

Takashi Kumagai, Zhen-Qing Chen

Publication date: 17 December 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-007-0070-5

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Upper bounds for symmetric Markov transition functions
• On reflected Dirichlet spaces
• Renaissance, recollements, mélanges, ralentissement de processus de Markov
• Dirichlet forms and symmetric Markov processes
• Drift transforms and Green function estimates for discontinuous processes
• Harnack inequality for some classes of Markov processes
• Harnack inequalities for jump processes
• Harnack's inequality for stable Lévy processes
• Ultracontractivity and Nash type inequalities
• On the Feller property of Dirichlet forms generated by pseudo differential operators
• Heat kernel estimates for stable-like processes on \(d\)-sets.
• Transition Probabilities for Symmetric Jump Processes
• NASH-TYPE INEQUALITIES AND HEAT KERNELS FOR NON-LOCAL DIRICHLET FORMS
• Heat kernel upper bounds for jump processes and the first exit time
• Non-local Dirichlet forms and symmetric jump processes
• Perturbation of Translation Invariant Positivity Preserving Semigroups on L 2 (R N )
• Symmetric Stable Laws and Stable-Like Jump-Diffusions
• Harnack inequalities for non-local operators of variable order
• A construction of markov processes by piecing out
• Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order

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