{"paper":{"title":"Isoperimetric Inequalities for Non-Local Dirichlet Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Jian Wang","submitted_at":"2017-06-13T11:52:01Z","abstract_excerpt":"Let $(E,\\F,\\mu)$ be a $\\si$-finite measure space. For a non-negative symmetric measure $J(\\d x, \\d y):=J(x,y) \\,\\mu(\\d x)\\,\\mu(\\d y)$ on $E\\times E,$ consider the quadratic form $$\\E(f,f):= \\frac{1}{2}\\int_{E\\times E} (f(x)-f(y))^2 \\, J(\\d x,\\d y)$$ in $L^2(\\mu)$. We characterize the relationship between the isoperimetric inequality and the super Poincar\\'e inequality associated with $\\E$. In particular, sharp Orlicz-Sobolev type and Poincar\\'e type isoperimetric inequalities are derived for stable-like Dirichlet forms on $\\R^n$, which include the existing fractional isoperimetric inequality a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04019","kind":"arxiv","version":2},"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"}