{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BCBSKD7NU6Y6DAXRHERFUX6A5X","short_pith_number":"pith:BCBSKD7N","schema_version":"1.0","canonical_sha256":"0883250feda7b1e182f139225a5fc0edf84f6282bd5e9c186de92fb1ad57887a","source":{"kind":"arxiv","id":"1601.03194","version":2},"attestation_state":"computed","paper":{"title":"An Improved Leray-Trudinger Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arka Mallick, Cyril Tintarev","submitted_at":"2016-01-13T10:37:43Z","abstract_excerpt":"In this article, we have derived the following Leray-Trudinger type inequality on a bounded domain $\\Omega$ in $\\mathbb{R}^n $ containing the origin. \\begin{align*} \\displaystyle{\\sup_{u\\in W^{1,n}_{0}(\\Omega), I_{n}[u,\\Omega,R]\\leq 1}}\\int_{\\Omega} e^{c_n\\left(\\frac{|u(x)|}{E_{2}^{\\beta}(\\frac{|x|}{R})}\\right)^{\\frac{n}{n-1}}} dx < +\\infty \\ \\text{, for some } c_n>0 \\ \\text{depending only on } n. \\end{align*} Here $\\beta = \\frac{2}{n}$, $I_n[u,\\Omega,R] := \\int_{\\Omega}|\\nabla u |^{n}dx- \\left(\\frac{n-1}{n}\\right)^{n}\\int_{\\Omega}\\frac{|u|^{n}}{|x|^{n}E_{1}^n(\\frac{|x|}{R})}dx $, $R \\geq \\dis"},"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":"1601.03194","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T10:37:43Z","cross_cats_sorted":[],"title_canon_sha256":"1a57bd8ddab7cc42f44a6232cc37983c59a533e7acadc306d45878040e11d18d","abstract_canon_sha256":"8f8c3cb837d5010f84d24800e19a47408a516e24ec85893e749b7136b04d4c4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:48.890375Z","signature_b64":"nRYcyxNgAv28hp4cqRBspq7sOVwm0KAa6ec2TnH4DUCFEfdOz88mcxdn+UXQqrOLL2Q9VoG3hTgNTOIH+ggEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0883250feda7b1e182f139225a5fc0edf84f6282bd5e9c186de92fb1ad57887a","last_reissued_at":"2026-05-18T01:18:48.889737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:48.889737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Improved Leray-Trudinger Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arka Mallick, Cyril Tintarev","submitted_at":"2016-01-13T10:37:43Z","abstract_excerpt":"In this article, we have derived the following Leray-Trudinger type inequality on a bounded domain $\\Omega$ in $\\mathbb{R}^n $ containing the origin. \\begin{align*} \\displaystyle{\\sup_{u\\in W^{1,n}_{0}(\\Omega), I_{n}[u,\\Omega,R]\\leq 1}}\\int_{\\Omega} e^{c_n\\left(\\frac{|u(x)|}{E_{2}^{\\beta}(\\frac{|x|}{R})}\\right)^{\\frac{n}{n-1}}} dx < +\\infty \\ \\text{, for some } c_n>0 \\ \\text{depending only on } n. \\end{align*} Here $\\beta = \\frac{2}{n}$, $I_n[u,\\Omega,R] := \\int_{\\Omega}|\\nabla u |^{n}dx- \\left(\\frac{n-1}{n}\\right)^{n}\\int_{\\Omega}\\frac{|u|^{n}}{|x|^{n}E_{1}^n(\\frac{|x|}{R})}dx $, $R \\geq \\dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03194","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":"1601.03194","created_at":"2026-05-18T01:18:48.889827+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.03194v2","created_at":"2026-05-18T01:18:48.889827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03194","created_at":"2026-05-18T01:18:48.889827+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCBSKD7NU6Y6","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCBSKD7NU6Y6DAXR","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCBSKD7N","created_at":"2026-05-18T12:30:07.202191+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/BCBSKD7NU6Y6DAXRHERFUX6A5X","json":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X.json","graph_json":"https://pith.science/api/pith-number/BCBSKD7NU6Y6DAXRHERFUX6A5X/graph.json","events_json":"https://pith.science/api/pith-number/BCBSKD7NU6Y6DAXRHERFUX6A5X/events.json","paper":"https://pith.science/paper/BCBSKD7N"},"agent_actions":{"view_html":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X","download_json":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X.json","view_paper":"https://pith.science/paper/BCBSKD7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.03194&json=true","fetch_graph":"https://pith.science/api/pith-number/BCBSKD7NU6Y6DAXRHERFUX6A5X/graph.json","fetch_events":"https://pith.science/api/pith-number/BCBSKD7NU6Y6DAXRHERFUX6A5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X/action/storage_attestation","attest_author":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X/action/author_attestation","sign_citation":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X/action/citation_signature","submit_replication":"https://pith.science/pith/BCBSKD7NU6Y6DAXRHERFUX6A5X/action/replication_record"}},"created_at":"2026-05-18T01:18:48.889827+00:00","updated_at":"2026-05-18T01:18:48.889827+00:00"}