Estimates of green functions for some perturbations of fractional laplacian

Illinois Journal of Mathematics

Volumn 51, Issue 4, 2008, Pages 1409-1438

  Grzywny, Tomasz ^a   Ryznar, Michal ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50949131174     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1258138552     Document Type: Article

References (18)

1. R. Bañuelos, Intrinsic ultracontractivity and eigenfunction estimates for Schrödinger operators, J. Funct. Anal. 100 (1991), 181-206. MR 1124298 (92k:35066)
2. K. Bogdan, The boundary Harnack principle for the fractional Laplacian, Studia Math. 123 (1997), 43-80. MR 1438304 (98g:31005)
3. _, Sharp estimates for the Green function in Lipschitz domains, J. Math. Anal. Appl. 243 (2000), 326-337. MR 1741527 (2001b:31007)
4. K. Bogdan and T. Byczkowski, Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains, Studia Math. 133 (1999), 53-92. MR 1671973 (99m:31010)
5. H. Byczkowska and T. Byczkowski, One-dimensional symmetric stable Feynman-Kac semigroups, Probab. Math. Statist. 21 (2001), 381-404. MR 1911445 (2003d:60092)
6. Z.-Q. Chen and R. Song, Intrinsic ultracontractivity and conditional gauge for symmetric stable processes, J. Funct. Anal. 150 (1997), 204-239. MR 1473631 (98j:60103)
7. _, Estimates on Green functions and Poisson kernels for symmetric stable processes, Math. Ann. 312 (1998), 465-501. MR 1654824 (2000b:60179)
8. _, Drift transforms and Green function estimates for discontinuous processes, J. Funct. Anal. 201 (2003), 262-281. MR 1986161 (2004c:60218)
9. K. L. Chung and Z. X. Zhao, From Brownian motion to Schrödinger's equation, Grundlehren der Mathematischen Wissenschaften, vol. 312, Springer-Verlag, Berlin, 1995. MR 1329992 (96f:60140)
10. T. Grzywny, Intrinsic ultracontractivity for Lévy processes, Probab. Math. Statist. 28 (2008), 91-106.
11. N. Ikeda and 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 (1962), 79-95. MR 0142153 (25 #5546)
12. T. Jakubowski, The estimates for the Green function in Lipschitz domains for the symmetric stable processes, Probab. Math. Statist. 22 (2002), 419-441. MR 1991120 (2004g:60069)
13. P. Kim and Y.-R. Lee, Generalized 3G theorem, and application to relativistic stable process on non-smooth open sets, J. Funct. Anal. 246 (2007), 113-134. MR 2316878
14. T. Kulczycki, Properties of Green function of symmetric stable processes, Probab. Math. Statist. 17 (1997), 339-364. MR 1490808 (98m:60119)
15. _, Intrinsic ultracontractivity for symmetric stable processes, Bull. Polish Acad. Sci. Math. 46 (1998), 325-334. MR 1643611 (99j:60115)
16. M. Ryznar, Estimates of Green function for relativistic α-stable process, Potential Anal. 17 (2002), 1-23. MR 1906405 (2003f:60087)
17. K.-I. Sato, Lévy processes and infinitely divisible distributions, Cambridge Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999, Translated from the 1990 Japanese original, Revised by the author. MR 1739520 (2003b:60064)
18. P. Sztonyk, On harmonic measure for Lévy processes, Probab. Math. Statist 20 (2000), 383-390. MR 1825650 (2002c:60126)