{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XTFRCVILPDGZAOMA3TRGHPMBTA","short_pith_number":"pith:XTFRCVIL","schema_version":"1.0","canonical_sha256":"bccb11550b78cd903980dce263bd81980bdcf959366a4e84d3af1924a6997f7c","source":{"kind":"arxiv","id":"1712.02044","version":2},"attestation_state":"computed","paper":{"title":"Hardy-Sobolev type inequalities and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen","submitted_at":"2017-12-06T05:32:00Z","abstract_excerpt":"This paper is devoted to various applications of Hardy-Sobolev type inequalities. We derive a new $L^2$ estimate for the $\\bar{\\partial}-$equation on ${\\mathbb C}^n$ which yields a quantitative generalization of the Hartogs extension theorem to the case when the singularity set is not necessary compact. We show that for any negative subharmonic function $\\psi$ on ${\\mathbb R}^n$, $n>2$, the BMO norm of $\\log |\\psi|$ is bounded above by $2\\sqrt{n-2}$ and $|\\psi|^\\gamma$ satisfies a reverse H\\\"older inequality for every $0<\\gamma<1$. We also show that every plurisubharmonic function is locally B"},"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":"1712.02044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-12-06T05:32:00Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e4428ade25852d57d9d94308558b72f03295865c8f613a57aa156fe4f2f07678","abstract_canon_sha256":"932b75be52498f1bc80f50e6b814677cd0ab5d33d333278ee0e7dfed41b38d2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:41.882488Z","signature_b64":"tmj1totoqxJuZPNrg+dnf2d+G4DKo0uIR1um1yKo9dntJnc0vDhNhfPOEYbxG91gVOujbP0I4fn6d+TJLbqpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bccb11550b78cd903980dce263bd81980bdcf959366a4e84d3af1924a6997f7c","last_reissued_at":"2026-05-18T00:24:41.881761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:41.881761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hardy-Sobolev type inequalities and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen","submitted_at":"2017-12-06T05:32:00Z","abstract_excerpt":"This paper is devoted to various applications of Hardy-Sobolev type inequalities. We derive a new $L^2$ estimate for the $\\bar{\\partial}-$equation on ${\\mathbb C}^n$ which yields a quantitative generalization of the Hartogs extension theorem to the case when the singularity set is not necessary compact. We show that for any negative subharmonic function $\\psi$ on ${\\mathbb R}^n$, $n>2$, the BMO norm of $\\log |\\psi|$ is bounded above by $2\\sqrt{n-2}$ and $|\\psi|^\\gamma$ satisfies a reverse H\\\"older inequality for every $0<\\gamma<1$. We also show that every plurisubharmonic function is locally B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02044","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":"1712.02044","created_at":"2026-05-18T00:24:41.881880+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.02044v2","created_at":"2026-05-18T00:24:41.881880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02044","created_at":"2026-05-18T00:24:41.881880+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTFRCVILPDGZ","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTFRCVILPDGZAOMA","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTFRCVIL","created_at":"2026-05-18T12:31:56.362134+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/XTFRCVILPDGZAOMA3TRGHPMBTA","json":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA.json","graph_json":"https://pith.science/api/pith-number/XTFRCVILPDGZAOMA3TRGHPMBTA/graph.json","events_json":"https://pith.science/api/pith-number/XTFRCVILPDGZAOMA3TRGHPMBTA/events.json","paper":"https://pith.science/paper/XTFRCVIL"},"agent_actions":{"view_html":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA","download_json":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA.json","view_paper":"https://pith.science/paper/XTFRCVIL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.02044&json=true","fetch_graph":"https://pith.science/api/pith-number/XTFRCVILPDGZAOMA3TRGHPMBTA/graph.json","fetch_events":"https://pith.science/api/pith-number/XTFRCVILPDGZAOMA3TRGHPMBTA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA/action/storage_attestation","attest_author":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA/action/author_attestation","sign_citation":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA/action/citation_signature","submit_replication":"https://pith.science/pith/XTFRCVILPDGZAOMA3TRGHPMBTA/action/replication_record"}},"created_at":"2026-05-18T00:24:41.881880+00:00","updated_at":"2026-05-18T00:24:41.881880+00:00"}