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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen

  2. Beijing Institute of Technology, Beijing, 100081, P. R. China

    Zhen-Qing Chen

  3. Department of Mathematics and Research Institute of Mathematics, Seoul National University, Seoul, 151-742, South Korea

    Panki Kim

  4. Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan

    Takashi Kumagai

Authors
  1. Zhen-Qing Chen
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  2. Panki Kim
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  3. Takashi Kumagai
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Corresponding author

Correspondence to Zhen-Qing Chen.

Additional information

The first author is partially supported by NSF (Grant No. DMS-0600206); The second author is partially supported by the Korea Science and Engineering Foundation (KOSEF) Grant funded by the Korea government (MEST) (No. R01-2008-000-20010-0); The third author is partially supported by the Grant-in-Aid for Scientific Research (B) 18340027

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

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  • DOI: https://doi.org/10.1007/s10114-009-8576-7

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