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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.04019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-13T11:52:01Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2c3ba21d982bc42dfbf376288992009193371c5c44d10551611023b8de6f9a0c","abstract_canon_sha256":"4483d1a233c5cafc38d0f49f9346c361c6cfe1fc9805e4ac6ffbbe2d071fb347"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:12.787068Z","signature_b64":"MUioqi5gFBbljhs7puBuvc3GGX6TuLC/36tNk7DPX5FGdnExpan7HE9wlL5nxri+jaUDZ9nx4qFvvbjhLUh4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b50c980b46b9b0ed801ff0667c381250ed48a39a7f477492d34236a56a87bc4b","last_reissued_at":"2026-05-18T00:40:12.786440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:12.786440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.04019","created_at":"2026-05-18T00:40:12.786536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.04019v2","created_at":"2026-05-18T00:40:12.786536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04019","created_at":"2026-05-18T00:40:12.786536+00:00"},{"alias_kind":"pith_short_12","alias_value":"WUGJQC2GXGYO","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WUGJQC2GXGYO3AA7","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WUGJQC2G","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD","json":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD.json","graph_json":"https://pith.science/api/pith-number/WUGJQC2GXGYO3AA76BTHYOASKD/graph.json","events_json":"https://pith.science/api/pith-number/WUGJQC2GXGYO3AA76BTHYOASKD/events.json","paper":"https://pith.science/paper/WUGJQC2G"},"agent_actions":{"view_html":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD","download_json":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD.json","view_paper":"https://pith.science/paper/WUGJQC2G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.04019&json=true","fetch_graph":"https://pith.science/api/pith-number/WUGJQC2GXGYO3AA76BTHYOASKD/graph.json","fetch_events":"https://pith.science/api/pith-number/WUGJQC2GXGYO3AA76BTHYOASKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD/action/storage_attestation","attest_author":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD/action/author_attestation","sign_citation":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD/action/citation_signature","submit_replication":"https://pith.science/pith/WUGJQC2GXGYO3AA76BTHYOASKD/action/replication_record"}},"created_at":"2026-05-18T00:40:12.786536+00:00","updated_at":"2026-05-18T00:40:12.786536+00:00"}