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References

  1. Bass, Richard F. Diffusions and elliptic operators.Probability and its Applications (New York). Springer-Verlag, New York, 1998. xiv+232 pp. ISBN: 0-387-98315-5 MR1483890 (99h:60136)
  2. M.T. Barlow, R.F. Bass, Z-Q. Chen, and M. Kassmann. Non-local Dirichlet forms and symmetric jump processes. to appear in Transactions of A.M.S.
  3. M.T. Barlow, A. Grigory'an, and T. Kumagai. Heat kernel upper bounds for jump processes and the first exit time. Preprint.
  4. Bass, Richard F.; Kassmann, Moritz. Harnack inequalities for non-local operators of variable order. Trans. Amer. Math. Soc. 357 (2005), no. 2, 837--850 (electronic). MR2095633 (2005i:60104)
  5. Bass, Richard F.; Levin, David A. Harnack inequalities for jump processes. Potential Anal. 17 (2002), no. 4, 375--388. MR1918242 (2003e:60194)
  6. Chen, Zhen-Qing; Kumagai, Takashi. Heat kernel estimates for stable-like processes on $d$-sets. Stochastic Process. Appl. 108 (2003), no. 1, 27--62. MR2008600 (2005d:60135)
  7. Chen, Zhen-Qing; Kumagai, Takashi. Heat kernel estimates for jump processes of mixed types on metric measure spaces. Probab. Theory Related Fields 140 (2008), no. 1-2, 277--317. MR2357678
  8. Z.Q. Chen, P. Kim, and T. Kumagai. Weighted Poincare inequality and heat kernel estimates for finite range jump processes. preprint.
  9. Z.Q. Chen, P. Kim, and R. Song. Heat kernel estimates for Dirichlet fractional laplacian. preprint.
  10. Z.Q. Chen, P. Kim, and R. Song. Two-sided heat kernel estimates for censored stable-like processes. preprint.
  11. Carlen, E. A.; Kusuoka, S.; Stroock, D. W. Upper bounds for symmetric Markov transition functions. Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), no. 2, suppl., 245--287. MR0898496 (88i:35066)
  12. Chen, Zhen-Qing; Song, Renming. Estimates on Green functions and Poisson kernels for symmetric stable processes. Math. Ann. 312 (1998), no. 3, 465--501. MR1654824 (2000b:60179)
  13. Chen, Ya-Zhe; Wu, Lan-Cheng. Second order elliptic equations and elliptic systems.Translated from the 1991 Chinese original by Bei Hu.Translations of Mathematical Monographs, 174. American Mathematical Society, Providence, RI, 1998. xiv+246 pp. ISBN: 0-8218-0970-9 MR1616087 (99i:35016)
  14. Davies, E. B. Heat kernels and spectral theory.Cambridge Tracts in Mathematics, 92. Cambridge University Press, Cambridge, 1989. x+197 pp. ISBN: 0-521-36136-2 MR0990239 (90e:35123)
  15. M. Foondun. Harmonic functions for a class of integro-differential operators. preprint.
  16. Fukushima, Masatoshi; Ōshima, Yōichi; Takeda, Masayoshi. Dirichlet forms and symmetric Markov processes.de Gruyter Studies in Mathematics, 19. Walter de Gruyter & Co., Berlin, 1994. x+392 pp. ISBN: 3-11-011626-X MR1303354 (96f:60126)
  17. De Giorgi, Ennio. Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari.(Italian) Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3) 3 1957 25--43. MR0093649 (20 #172)
  18. M. Kassmann. The classical Harnack inequality fails for non-local operators. preprint.
  19. Kassmann, Moritz. On regularity for Beurling-Deny type Dirichlet forms. Potential Anal. 19 (2003), no. 1, 69--87. MR1962952 (2004a:31005)
  20. Krylov, N. V.; Safonov, M. V. An estimate for the probability of a diffusion process hitting a set of positive measure.(Russian) Dokl. Akad. Nauk SSSR 245 (1979), no. 1, 18--20. MR0525227 (80b:60101)
  21. Meyer, P. A. Renaissance, recollements, mélanges, ralentissement de processus de Markov.(French) Collection of articles dedicated to Marcel Brelot on the occasion of his 70th birthday. Ann. Inst. Fourier (Grenoble) 25 (1975), no. 3-4, xxiii, 465--497. MR0415784 (54 #3862)
  22. Moser, Jürgen. On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. 14 1961 577--591. MR0159138 (28 #2356)
  23. Moser, Jürgen. A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math. 17 1964 101--134. MR0159139 (28 #2357)
  24. Nash, J. Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 80 1958 931--954. MR0100158 (20 #6592)
  25. Rao, Murali; Song, Renming; Vondraček, Zoran. Green function estimates and Harnack inequality for subordinate Brownian motions. Potential Anal. 25 (2006), no. 1, 1--27. MR2238934 (2008g:60235)
  26. Saloff-Coste, L.; Stroock, D. W. Opérateurs uniformément sous-elliptiques sur les groupes de Lie.(French) [Uniformly subelliptic operators on Lie groups] J. Funct. Anal. 98 (1991), no. 1, 97--121. MR1111195 (92k:58264)
  27. Song, Renming; Vondraček, Zoran. Harnack inequality for some discontinuous Markov processes with a diffusion part. Glas. Mat. Ser. III 40(60) (2005), no. 1, 177--187. MR2195869 (2008k:60181)


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