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We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.
Riesz, M.M. (1938). Intégrales de Riemann–Liouville et potentiels. Acta Sci. Math. Szeged. 9 1–42
1938
Earlier work this paper cites.
Blumenthal, R. M.R. M. andGetoor, R. K.R. K. (1960). Some theorems on stable processes. Trans. Amer. Math. Soc. 95 263–273
1960
Earlier work this paper cites.
Blumenthal, R. M.R. M., Getoor, R. K.R. K. andRay, D. B.D. B. (1961). On the distribution of first hits for the symmetric stable processes. Trans. Amer. Math. Soc. 99 540–554
1961
Earlier work this paper cites.
Ikeda, NobuyukiN. andWatanabe, ShinzoS. (1962). On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes. J. Math. Kyoto Univ. 2 79–95
1962
Earlier work this paper cites.
Bogdan, KrzysztofK., Byczkowski, TomaszT., Kulczycki, TadeuszT., Ryznar, MichalM., Song, RenmingR. andVondraček, ZoranZ. (2009). Potential Analysis of Stable Processes and Its Extensions (P. Graczyk and A. Stos, eds.). Lecture Notes in Math. 1980. Springer, Berlin
1980
Earlier work this paper cites.
Zhao, Zhong XinZ. X. (1986). Green function for Schrödinger operator and conditioned Feynman–Kac gauge. J. Math. Anal. Appl. 116 309–334
1986
Earlier work this paper cites.
Kulczycki, TadeuszT. (1997). Properties of Green function of symmetric stable processes. Probab. Math. Statist. 17 339–364
1997
Earlier work this paper cites.
Chen, Zhen-QingZ.-Q. andSong, RenmingR. (1998). Estimates on Green functions and Poisson kernels for symmetric stable processes. Math. Ann. 312 465–501
1998
Earlier work this paper cites.
Kulczycki, TadeuszT. (1998). Intrinsic ultracontractivity for symmetric stable processes. Bull. Polish Acad. Sci. Math. 46 325–334
1998
Earlier work this paper cites.
Bogdan, KrzysztofK. andByczkowski, TomaszT. (1999). Potential theory for the α \alpha -stable Schrödinger operator on bounded Lipschitz domains. Studia Math. 133 53–92
1999
Earlier work this paper cites.
Sato, Ken-itiK.-i. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics 68. Cambridge Univ. Press, Cambridge
1999
Earlier work this paper cites.
Song, RenmingR. andWu, Jang-MeiJ.-M. (1999). Boundary Harnack principle for symmetric stable processes. J. Funct. Anal. 168 403–427
1999
Earlier work this paper cites.
Bogdan, KrzysztofK. (2000). Sharp estimates for the Green function in Lipschitz domains. J. Math. Anal. Appl. 243 326–337
2000
Earlier work this paper cites.
Bogdan, KrzysztofK. andByczkowski, TomaszT. (2000). Potential theory of Schrödinger operator based on fractional Laplacian. Probab. Math. Statist. 20 293–335
2000
Earlier work this paper cites.
Bogdan, K.K., Kulczycki, T.T. andNowak, AdamA. (2002). Gradient estimates for harmonic and q q -harmonic functions of symmetric stable processes. Illinois J. Math. 46 541–556
2002
Earlier work this paper cites.
Jakubowski, TomaszT. (2002). The estimates for the Green function in Lipschitz domains for the symmetric stable processes. Probab. Math. Statist. 22 419–441
2002
Cited alongside, same era.
Zhang, Qi S.Q. S. (2002). The boundary behavior of heat kernels of Dirichlet Laplacians. J. Differential Equations 182 416–430
2002
Cited alongside, same era.
Bogdan, KrzysztofK., Stós, AndrzejA. andSztonyk, PawełP. (2003). Harnack inequality for stable processes on d d -sets. Studia Math. 158 163–198
2003
Cited alongside, same era.
Varopoulos, N. Th.N. T. (2003). Gaussian estimates in Lipschitz domains. Canad. J. Math. 55 401–431
2003
Cited alongside, same era.
Bañuelos, RodrigoR. andBogdan, KrzysztofK. (2004). Symmetric stable processes in cones. Potential Anal. 21 263–288
2004
Cited alongside, same era.
Bañuelos, RodrigoR. andKulczycki, TadeuszT. (2008). Trace estimates for stable processes. Probab. Theory Related Fields 142 313–338
2008
Later among the works it cites.
Bogdan, KrzysztofK., Hansen, WolfhardW. andJakubowski, TomaszT. (2008). Time-dependent Schrödinger perturbations of transition densities. Studia Math. 189 235–254
2008
Later among the works it cites.
Bogdan, KrzysztofK., Kulczycki, TadeuszT. andKwaśnicki, MateuszM. (2008). Estimates and structure of α \alpha -harmonic functions. Probab. Theory Related Fields 140 345–381
2008
Later among the works it cites.
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
2008
Later among the works it cites.
Grigor’yan, AlexanderA. andHu, JiaxinJ. (2008). Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Invent. Math. 174 81–126
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Bogdan, K.K. andŻak, T.T. (2006). On Kelvin transformation. J. Theoret. Probab. 19 89–120
2006
Cited alongside, same era.
Hansen, WolfhardW. (2006). Global comparison of perturbed Green functions. Math. Ann. 334 643–678
2006
Cited alongside, same era.
Kulczycki, TadeuszT. andSiudeja, BartłomiejB. (2006). Intrinsic ultracontractivity of the Feynman–Kac semigroup for relativistic stable processes. Trans. Amer. Math. Soc. 358 5025–5057 (electronic)
2006
Cited alongside, same era.
Michalik, KrzysztofK. (2006). Sharp estimates of the Green function, the Poisson kernel and the Martin kernel of cones for symmetric stable processes. Hiroshima Math. J. 36 1–21
2006
Cited alongside, same era.
Rao, MuraliM., Song, RenmingR. andVondraček, ZoranZ. (2006). Green function estimates and Harnack inequality for subordinate Brownian motions. Potential Anal. 25 1–27
2006
Cited alongside, same era.
Siudeja, BartłomiejB. (2006). Symmetric stable processes on unbounded domains. Potential Anal. 25 371–386
2006
Cited alongside, same era.
Bogdan, KrzysztofK. andJakubowski, TomaszT. (2007). Estimates of heat kernel of fractional Laplacian perturbed by gradient operators. Comm. Math. Phys. 271 179–198
2007
Cited alongside, same era.
2008
Later among the works it cites.
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
2008
Later among the works it cites.
Barlow, Martin T.M. T., Grigor’yan, AlexanderA. andKumagai, TakashiT. (2009). Heat kernel upper bounds for jump processes and the first exit time. J. Reine Angew. Math. 626 135–157
2009
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2009
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Chen, Zhen-QingZ.-Q. andTokle, J.J. (2009). Global heat kernel estimates for fractional Laplacians in unbounded open sets. Probab. Theory Related Fields. DOI: 10.1007/s00440-009-0256-0 . To appear
2009
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Kulczycki, T.T., Kwaśnicki, M.M., Małecki, J.J. andStós, A.A. (2009). Spectral properties of the Cauchy process on half-line and interval. Proc. London Math. Soc
2009
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Kwaśnicki, MateuszM. (2009). Intrinsic ultracontractivity for stable semigroups on unbounded open sets. Potential Anal. 31 57–77
2009
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2009
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Bogdan, K.K. andGrzywny, T.T. (2010). Heat kernel of fractional Laplacian in cones. Colloq. Math. 118 365–377
2010
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Chen, Z. Q.Z. Q., Kim, P.P. andSong, R.R. (2010). Heat kernel estimates for Dirichlet fractional Laplacian. J. European Math. Soc
2010
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