Estimates of Green Function for some perturbations of fractional Laplacian

Details Estimates of Green Function for some perturbations of fractional Laplacian Estimates of Green Function for some perturbations of fractional Laplacian

2006-05-14

arxiv.org/abs/math/0605370v1

Illinois J. Math. 51(4), 1409-1438 (2007)

Mathematics

Probability

28 pages

Scientific paper

Suppose that Y(t) is a d-dimensional Levy symmetric process for which its Levy measure differs from the Levy measure of the isotropic alpha-stable process (00, we prove that the Green functions are comparable, provided D is connected. These results apply for example to alpha-stable relativistic process. This process was studied in recent years. In the paper we also considered one dimensional case for alpha<= 1 and proved that the Green functions for an open and bounded interval are comparable.

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