{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PQQ5JGO7EQXLVHC32SFQHOOWX2","short_pith_number":"pith:PQQ5JGO7","schema_version":"1.0","canonical_sha256":"7c21d499df242eba9c5bd48b03b9d6be8f1ca98baf3e0a516a73c90dc2b7f391","source":{"kind":"arxiv","id":"1510.06662","version":1},"attestation_state":"computed","paper":{"title":"Moser functions and fractional Moser-Trudinger type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Hyder","submitted_at":"2015-10-22T15:51:05Z","abstract_excerpt":"We improve the sharpness of some fractional Moser-Trudinger type inequalities, particularly those studied by Lam-Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to the problem $(-\\Delta)^\\frac{n}{2}u=\\lambda ue^{bu^2} \\,\\text{ in }\\Omega,\\, 0<\\lambda<\\lambda_1,\\,b>0,$ with Dirichlet boundary condition, for any domain $\\Omega$ in $\\mathbb{R}^n$ with finite measure. Here $\\lambda_1$ is the first eigenvalue of $(-\\Delta)^\\frac n2$ on $\\Omega$."},"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":"1510.06662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-22T15:51:05Z","cross_cats_sorted":[],"title_canon_sha256":"aa02c17d580fb6b86b6a097e0c5be14009759f762ecc91e40eec065c5a7193da","abstract_canon_sha256":"4f1a5a7a9d4d10dfde42c51805269b6a3668c89d02d1d4e05a56d84bf908e74a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:30.333271Z","signature_b64":"DpDx1fXSlxo+WCE5OCyy9UnI7uVb6Hmt81nJs2+024wReub829yP1uyzRA/Hm7V/DWawT51D+PkPssfIEQaDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c21d499df242eba9c5bd48b03b9d6be8f1ca98baf3e0a516a73c90dc2b7f391","last_reissued_at":"2026-05-18T01:29:30.332673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:30.332673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moser functions and fractional Moser-Trudinger type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Hyder","submitted_at":"2015-10-22T15:51:05Z","abstract_excerpt":"We improve the sharpness of some fractional Moser-Trudinger type inequalities, particularly those studied by Lam-Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to the problem $(-\\Delta)^\\frac{n}{2}u=\\lambda ue^{bu^2} \\,\\text{ in }\\Omega,\\, 0<\\lambda<\\lambda_1,\\,b>0,$ with Dirichlet boundary condition, for any domain $\\Omega$ in $\\mathbb{R}^n$ with finite measure. Here $\\lambda_1$ is the first eigenvalue of $(-\\Delta)^\\frac n2$ on $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06662","kind":"arxiv","version":1},"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":"1510.06662","created_at":"2026-05-18T01:29:30.332753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06662v1","created_at":"2026-05-18T01:29:30.332753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06662","created_at":"2026-05-18T01:29:30.332753+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQQ5JGO7EQXL","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQQ5JGO7EQXLVHC3","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQQ5JGO7","created_at":"2026-05-18T12:29:37.295048+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/PQQ5JGO7EQXLVHC32SFQHOOWX2","json":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2.json","graph_json":"https://pith.science/api/pith-number/PQQ5JGO7EQXLVHC32SFQHOOWX2/graph.json","events_json":"https://pith.science/api/pith-number/PQQ5JGO7EQXLVHC32SFQHOOWX2/events.json","paper":"https://pith.science/paper/PQQ5JGO7"},"agent_actions":{"view_html":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2","download_json":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2.json","view_paper":"https://pith.science/paper/PQQ5JGO7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06662&json=true","fetch_graph":"https://pith.science/api/pith-number/PQQ5JGO7EQXLVHC32SFQHOOWX2/graph.json","fetch_events":"https://pith.science/api/pith-number/PQQ5JGO7EQXLVHC32SFQHOOWX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2/action/storage_attestation","attest_author":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2/action/author_attestation","sign_citation":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2/action/citation_signature","submit_replication":"https://pith.science/pith/PQQ5JGO7EQXLVHC32SFQHOOWX2/action/replication_record"}},"created_at":"2026-05-18T01:29:30.332753+00:00","updated_at":"2026-05-18T01:29:30.332753+00:00"}