{"paper":{"title":"Estimates of Green Function for some perturbations of fractional Laplacian","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Micha{\\l} Ryznar, Tomasz Grzywny","submitted_at":"2006-05-14T22:24:11Z","abstract_excerpt":"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 (0<alpha<2) by a finite signed measure. For a bounded Lipschitz set D we compare the Green functions of the process Y and its stable counterpart. We prove a few comparability results either one sided or two sided. Assuming an additional condition about the difference of the densities of the Levy measures, namely that it is of order of |x|^{-d+varrho} as x near 0, where varrho>0, we prove that the Green functions are comparable, provided D is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605370","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}