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In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators $m-(m^{2/\alpha}-\Delta)^{\alpha/2}$] in $C^{1,1}$ open sets.
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Chen, Zhen-QingZ.-Q. andKumagai, TakashiT. (2008). Heat kernel estimates for jump processes of mixed types on metric measure spaces. Probab. Theory Related Fields 140 277–317
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Chen, Zhen-QingZ.-Q. andSong, RenmingR. (2005). Two-sided eigenvalue estimates for subordinate processes in domains. J. Funct. Anal. 226 90–113
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Chen, Zhen-QingZ.-Q. andSong, RenmingR. (2006). Continuity of eigenvalues of subordinate processes in domains. Math. Z. 252 71–89
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Kim, PankiP. (2006). Relative Fatou’s theorem for ( − Δ ) α / 2 (-\Delta)^{\alpha/2} -harmonic functions in bounded κ \kappa -fat open sets. J. Funct. Anal. 234 70–105
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Kulczycki, TadeuszT. andSiudeja, BartłomiejB. (2006). Intrinsic ultracontractivity of the Feynman–Kac semigroup for relativistic stable processes. Trans. Amer. Math. Soc. 358 5025–5057
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Grzywny, TomaszT. andRyznar, MichałM. (2008). Two-sided optimal bounds for Green functions of half-spaces for relativistic α \alpha -stable process. Potential Anal. 28 201–239
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Byczkowski, T.T., Małecki, J.J. andRyznar, M.M. (2009). Bessel potentials, hitting distributions and Green functions. Trans. Amer. Math. Soc. 361 4871–4900
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Chen, Zhen-QingZ.-Q. (2009). Symmetric jump processes and their heat kernel estimates. Sci. China Ser. A 52 1423–1445
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Chen, Zhen-QingZ.-Q., Kim, PankiP. andKumagai, TakashiT. (2009). On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces. Acta Math. Sin. (Engl. Ser.) 25 1067–1086
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Chen, Z. Q.Z. Q., Kim, P.P. andSong, R.R. (2010). Green function estimates for relativistic stable processes in half-space-like open sets. Preprint
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Chen, Zhen-QingZ.-Q., Kim, PankiP. andSong, RenmingR. (2010). Heat kernel estimates for the Dirichlet fractional Laplacian. J. Eur. Math. Soc. (JEMS) 12 1307–1329
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Chen, Zhen-QingZ.-Q., Kim, PankiP. andSong, RenmingR. (2010). Two-sided heat kernel estimates for censored stable-like processes. Probab. Theory Related Fields 146 361–399
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Chen, Z. Q.Z. Q. andTokle, J.J. (2010). Global heat kernel estimates for fractional Laplacians in unbounded open sets. Probab. Theory Related Fields
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Sztonyk, PawełP. (2010). Estimates of tempered stable densities. J. Theoret. Probab. 23 127–147
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Chen, Z. Q.Z. Q., Kim, P.P. andKumagai, T.T. (2011). Global heat kernel estimates for symmetric jump processes. Trans. Amer. Math. Soc
2011
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