Estimates of Green functions for some perturbations of fractional Laplacian
Tomasz Grzywny, Michał Ryznar · Illinois Journal of Mathematics · 2007
Suppose that $Y_t$ is a $d$-dimensional symmetric Lévy process such that its Lévy measure differs from the Lévy measure of the isotropic $\alpha$-stable process ($0 0$, we prove that the Green functions are comparable, provided $D$ is connected. These results apply, for example, to the relativistic $\alpha$-stable process. The bounds for its Green functions were previously known for $d > \alpha$ and smooth sets. Here we consider also the one-dimensional case for $\alpha \ge 1$, and we prove that the Green functions for a bounded open interval are comparable, a case that, to the best of our knowledge, had not been treated in the literature.