Estimates on Green functions and Poisson kernels for symmetric stable processes

Mathematische Annalen

Volumn 312, Issue 3, 1998, Pages 465-501

  Chen, Zhen Qing ^a   Song, Renming ^b  

^a Department of Obstetrics Gynecology   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032335134     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050232     Document Type: Article

References (23)

1. J. Bertoin: Lévy Processes, Cambridge University Press, 1996.
2. R. M. Blumenthal, R. K. Getoor: Markov Processes and Potential Theory, Academic Press, 1968.
3. R. M. Blumenthal, R. K. Getoor, D. B. Ray: On the distribution of first hits for the symmetric stable processes, Trans. Amer. Math. Soc. 99 (1961), 540-554.
4. K. Bogdan: The boundary Harnack principle for the fractional Laplacian, Studia Math. 123(1) (1997), 43-80.
5. Z. Q. Chen, R. Song: Intrinsic, ultracontractivity and conditional gauge for symmetric stable processes, J. Funct. Analysis 150 (1997), 204-239.
6. K. L. Chung, Z. Zhao: From Brownian motion to Schrödinger's equation (1995), Springer, Berlin
7. M. Cranston: Lifetime of conditional Brownian motion in Lipschitz domains, Z. Wahrsch. Verw. Gebiete. 70 (1985), 335-340.
8. M. Cranston, E. Fabes, Z. Zhao: Conditional gauge and potential theory for the Schrödinger operator., Trans. Amer. Math. Soc. 307 (1988), 174-194.
9. J. Elliott: Dirichlet spaces associated with integro-differential operators, Part 1, 111. J. Math. 9 (1965), 87-98.
10. J. Elliott: Dirichlet spaces associated with integro-differential operators, Part II 111. J. Math. 10 (1966), 66-89.
11. M. Fukushima, Y. Oshima, M. Takeda: Dirichlet forms and Symmetric Markov Processes, Walter de Gruyter, 1994.
12. R. Getoor: First passage times for symmetric stable processes in space Trans. Amer. Math. Soc. 101 (1961), 75-90.
13. N. Ikeda, S. Watanabe: On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes J. Math. Kyoto Univ. 2-1 (1962), 79-95.
14. A. Janicki, A. Weron: Simulation and Chaotic Behavior of α-Stable Processes, Dekker, 1994.
15. J. Klafter, M. F. Shlesinger, G. Zumofen: Beyond Brownian motion., Physics Today 49 No. 2 (1996), 33-39.
16. N. S. Landkof: Foundations of Modern Potential Theory, Springer-Verlag, 1970.
17. H. P. McKean: Sample functions of stable processes, Ann. Math. 61 (1955), 564-579.
18. P. W. Millar: First passage distributions of processes with independent increments, Ann. Prob. 3 (1975), 215-233.
19. M. Sharpe: General theory of Markov processes, Academic Press, 1988.
20. M. L. Silverstein: Symmetric Markov Processes, Springer-Verlag, 1974.
21. M. L. Silverstein: Boundary Theory for Symmetric Markov Processes, Springer-Verlag, 1976.
22. Z. Zhao: Uniform boundedness of conditional gauge and Schrödinger equations, Commun. Math. Phys. 93 (1984), 19-31.
23. Z. Zhao: Green function for Schrödinger operator and conditioned Feynman-Kac gauge, J. Math. Anal. Appl. 116 (1986), 309-334.