Bessel potentials, hitting distributions and green functions

Transactions of the American Mathematical Society

Volumn 361, Issue 9, 2009, Pages 4871-4900

  Byczkowski, T ^a   Malecki J ^a   Ryznar, M ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68749083442     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-09-04657-1     Document Type: Article

References (26)

1. R. Adams, N. Aronszajn and K. T. Smith, Theory of Bessel potentials. II, Ann. Inst. Fourier 17 (1967), 1-135. MR0228702 (37:4281)
2. N. Aronszajn and K. T. Smith, Theory of Bessel potentials. I, Ann. Inst. Fourier 11 (1961), 385-475. MR0143935 (26:1485)
3. P. Billingsley, Probability and Measure, J. Wiley, New York, 1979. MR534323 (80h:60001)
4. R. M. Blumenthal and R. K. Getoor, MarkovProcesses and Potential Theory, Springer, New York, 1968. MR0264757 (41:9348)
5. R. M. Blumenthal, R. K. Getoor and D. B. Ray, On the distribution of first hits for the symmetric stable processes, Trans. Amer. Math. Soc. 99 (1961), 540-554. MR0126885 (23:a4179)
6. N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1989. MR1015093 (90i:26003)
7. R. Carmona, W. C. Masters and B. Simon, Relativistic Schrödinger operators; Asymptotic behaviour of the eigenfunctions, J. Funct. Anal. 91 (1990), 117-142. MR1054115 (91i:35139)
8. K. L. Chung and Z. Zhao, From Brownian motion to Schrödinger's equation, SpringerVerlag, New York, 1995. MR1329992 (96f:60140)
9. Z.-Q. Chen and R. Song, Drift transforms and Green function estimates for discontinuous processes, J. Funct. Anal. 201 (2003), 262-281. MR1986161 (2004c:60218)
10. Erdelyiet al., eds., Higher Transcendental Functions, vol. II, McGraw-Hill, New York, 1953-1955. MR0066496 (16:586c)
11. th edition, Academic Press (London), 2000. MR0197789 (33:5952)
12. E. Lieb, The stability of matter: From atoms to stars, Bull. Amer. Math. Soc. 22 (1990), 1-49. MR1014510 (91f:81002)
13. T. Grzywny, Potential theory for α-stable relativistic process, Master Thesis, Institut of Mathematics and Computer Sciences, Wroclaw University of Technology, 2005.
14. T. Grzywny and M. Ryznar, Estimates of Green function for some perturbations of fractional Laplacian, Illinois J. Math. 51 (2007), no. 4, 1409-1438. MR2417435
15. T. Grzywny and M. Ryznar, Optimal estimates of Green function of half-spaces for relativistic process, Potential Anal. 28(3) (2008), 201-239. MR2386098 (2009b:60241)
16. nd edition, Springer-Verlag, 1983. MR717035 (85g:35002a)
17. N. Ikeda and S. Watanabe, On some relations between the harmonic measure and the L évy measure for a certain class of Markov processes, J. Math. Kyoto Univ. 2 (1962), 79-95. MR0142153 (25:5546)
18. P. Kim and Y.-R. Lee, Generalized 3G theorem and application to relativistic stable process on non-smooth open sets, J. Funct. Anal. 246(1) (2007), 113-143. MR2316878 (2008h:60316)
19. T. Kulczyckiand B. Siudeja, Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes, Trans. Amer. Math. Soc. 358(11) (2006), 5025-5057. MR2231884 (2007m:47098)
20. N. S. Landkof, Foundations of Modern Potential Theory, Springer, New York, 1972. MR0350027 (50:2520)
21. M. Rao, R. Song and Z. Vondracek, Green function estimates and Harnack inequality for subordinate Brownian motions, Potential Anal. 25 (2006), no. 1, 1-27. MR2238934 (2008g:60235)
22. D. B. Ray, Stable processes with an absorbing barrier, Trans. Amer. Math. Soc. 89 (1958), 16-24. MR0105178 (21:3921)
23. M. Ryznar, Estimate of Green function for relativistic α-stable processes, Potential Anal. 17 (2002), 1-23. MR1906405 (2003f:60087)
24. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series 30, Princeton, NJ, 1970. MR0290095 (44:7280)
25. K. I. Sato, Lévy processes and infinitely divisible distributions, Cambridge University Press, 1999. MR1739520 (2003b:60064)
26. P. Sztonyk, On harmonic measure for Lévy process, Probab. Math. Statist. 20 (2000), 383-390. MR1825650 (2002c:60126)