{"paper":{"title":"Spatial regularity of semigroups generated by L\\'{e}vy type operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Mingjie Liang","submitted_at":"2018-04-11T02:08:20Z","abstract_excerpt":"We apply the probabilistic coupling approach to establish the spatial regularity of semigroups associated with L\\'{e}vy type operators, by assuming that the martingale problem of L\\'{e}vy type operators is well posed. In particular, we can prove the Lipschitz continuity of the semigroups under H\\\"{o}lder continuity of coefficients, even when the L\\'evy kernel corresponding to L\\'{e}vy type operators is singular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03781","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"}