On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces

Zhen Qing Chen*, Panki Kim, Takashi Kumagai

*Corresponding author for this work

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Abstract

In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.

Original languageEnglish
Pages (from-to)1067-1086
Number of pages20
JournalActa Mathematica Sinica, English Series
Volume25
Issue number7
DOIs
Publication statusPublished - Jul 2009

Keywords

  • Dirichlet form
  • Heat kernel estimates
  • Jump process
  • Jumping kernel
  • Parabolic Harnack inequality

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Chen, Z. Q., Kim, P., & Kumagai, T. (2009). On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces. Acta Mathematica Sinica, English Series, 25(7), 1067-1086. https://doi.org/10.1007/s10114-009-8576-7