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Green function estimates for relativistic stable processes in half-space-like open sets

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  • Chen, Zhen-Qing
  • Kim, Panki
  • Song, Renming

Abstract

In this paper, we establish sharp two-sided estimates for the Green functions of relativistic stable processes (i.e. Green functions for non-local operators m-(m2/[alpha]-[Delta])[alpha]/2) in half-space-like C1,1 open sets. The estimates are uniform in m[set membership, variant](0,M] for each fixed M[set membership, variant](0,[infinity]). When m[downwards arrow]0, our estimates reduce to the sharp Green function estimates for -(-[Delta])[alpha]/2 in such kind of open sets that were obtained recently in Chen and Tokle [12]. As a tool for proving our Green function estimates, we show that a boundary Harnack principle for Xm, which is uniform for all m[set membership, variant](0,[infinity]), holds for a large class of non-smooth open sets.

Suggested Citation

  • Chen, Zhen-Qing & Kim, Panki & Song, Renming, 2011. "Green function estimates for relativistic stable processes in half-space-like open sets," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1148-1172, May.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:5:p:1148-1172
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    2. Kim, Panki & Song, Renming & Vondracek, Zoran, 2009. "Boundary Harnack principle for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1601-1631, May.
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