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Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results

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Dirichlet Forms and Related Topics (IWDFRT 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 394))

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Abstract

This article gives an overview of some recent progress in the study of sharp two-sided estimates for the transition density of a large class of Markov processes having both diffusive and jumping components in metric measure spaces. We summarize some of the main results obtained recently in [11, 18] and provide several examples. We also discuss new ideas of the proof for the off-diagonal upper bounds of transition densities which are based on a generalized Davies’ method developed in [10].

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Acknowledgements

The research of Zhen-Qing Chen is partially supported by Simons Foundation Grant 520542. The research of Panki Kim is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1E1A1A01941893). The research of Takashi Kumagai is supported by JSPS KAKENHI Grant Number JP17H01093 and JP22H00099. The research of Jian Wang is supported by the National Natural Science Foundation of China (Nos. 11831014 and 12071076), the Program for Probability and Statistics: Theory and Application (No. IRTL1704) and the Program for Innovative Research Team in Science and Technology in Fujian Province University (IRTSTFJ).

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Authors and Affiliations

  1. University of Washington, Seattle, USA

    Zhen-Qing Chen

  2. Seoul National University, Seoul, South Korea

    Panki Kim

  3. Waseda University, Tokyo, Japan

    Takashi Kumagai

  4. Fujian Normal University, Fuzhou, China

    Jian Wang

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

Correspondence to Takashi Kumagai .

Editor information

Editors and Affiliations

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

    Zhen-Qing Chen

  2. Department of Mathematics, Kansai University, Osaka, Japan

    Masayoshi Takeda

  3. Department of Mathematics, Kansai University, Osaka, Japan

    Toshihiro Uemura

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Chen, ZQ., Kim, P., Kumagai, T., Wang, J. (2022). Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results. In: Chen, ZQ., Takeda, M., Uemura, T. (eds) Dirichlet Forms and Related Topics. IWDFRT 2022. Springer Proceedings in Mathematics & Statistics, vol 394. Springer, Singapore. https://doi.org/10.1007/978-981-19-4672-1_5

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