{"paper":{"title":"Intrinsic Ultracontractivity for General L\\'evy processes on Bounded Open Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Xin Chen","submitted_at":"2015-01-25T08:39:28Z","abstract_excerpt":"We prove that a general (not necessarily symmetric) L\\'evy process killed on exiting a bounded open set (without regular condition on the boundary) is intrinsically ultracontractive, provided that $B(0,R_0)\\subseteq \\rm{supp}(\\nu)$ for some constant $R_0>0$, where $\\rm{supp}(\\nu)$ denotes the support of the associated L\\'evy measure $\\nu$. For a symmetric L\\'evy process killed on exiting a bounded H\\\"older domain of order $0$, we also obtain the intrinsic ultracontractivity under much weaker assumption on the associated L\\'evy measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06130","kind":"arxiv","version":3},"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"}