Geodesic
Estimates for the distribution of the first exit time of α-stable processes
Discussiones Mathematicae. Probability and Statistics, Tome 22 (2002) no. 1-2, pp. 53-59.

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The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes.
Keywords: first exit time, α-stable processes 
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Cupała, Wiesław. Estimates for the distribution of the first exit time of α-stable processes. Discussiones Mathematicae. Probability and Statistics, Tome 22 (2002) no. 1-2, pp. 53-59. http://geodesic.mathdoc.fr/item/DMPS_2002_22_1-2_a4/

[1] D. Levin and M. Solomyak, Rozenblum-Lieb-Cwikel inequality for Markov generators, J. d'Anal. Math. 71 (1997), 173-193.

[2] N.T. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260.