{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5OJWYL5RJ4EET52V72LINSHXDF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"00d71e41329ec4f5a5fde4fa2b0b58c4d9c1ae15061a854a9ae910add032808c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-09T02:30:04Z","title_canon_sha256":"7405ff8f20a81e2be92074aae1377363f9daf021ee234bc84cb45452ae489f3b"},"schema_version":"1.0","source":{"id":"1702.02682","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02682","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02682v2","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02682","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"5OJWYL5RJ4EE","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5OJWYL5RJ4EET52V","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5OJWYL5R","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:45a4bb68f1651c374837ae3bf95d9b73ce210b09eedc537a98b785b9527d2efd","target":"graph","created_at":"2026-05-18T00:23:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the weighted norm inequality of $(1,q)$-type,\n  \\[ \\Vert \\mathbf{G}\\nu \\Vert_{L^q(\\Omega, d\\sigma)} \\le C \\Vert \\nu \\Vert, \\quad \\text{ for all } \\nu \\in \\mathcal{M}^+(\\Omega), \\] along with its weak-type analogue, for $0 < q < 1$, where $\\mathbf{G}$ is an integral operator associated with the nonnegative kernel $G(x,y)$. Here $\\mathcal{M}^+(\\Omega)$ denotes the class of positive Radon measures in $\\Omega$; $\\sigma, \\nu \\in \\mathcal{M}^+(\\Omega)$, and $||\\nu||=\\nu(\\Omega)$.\n  For both weak-type and strong-type inequalities, we provide conditions which characterize the measures $\\sigma","authors_text":"Igor E. Verbitsky, Stephen Quinn","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-09T02:30:04Z","title":"A sublinear version of Schur's lemma and elliptic PDE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02682","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:923e625c3ce925e0dcbb34ab4043dbdca4a070f465974264e386600f06e2af9e","target":"record","created_at":"2026-05-18T00:23:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"00d71e41329ec4f5a5fde4fa2b0b58c4d9c1ae15061a854a9ae910add032808c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-09T02:30:04Z","title_canon_sha256":"7405ff8f20a81e2be92074aae1377363f9daf021ee234bc84cb45452ae489f3b"},"schema_version":"1.0","source":{"id":"1702.02682","kind":"arxiv","version":2}},"canonical_sha256":"eb936c2fb14f0849f755fe9686c8f71963e1ea5fed048659f8c06d32ee6c78df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb936c2fb14f0849f755fe9686c8f71963e1ea5fed048659f8c06d32ee6c78df","first_computed_at":"2026-05-18T00:23:45.957050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:45.957050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Qbq1GjWfgKrAjXBimLtiSywMxkqxzr6ngtUyRCwnF8VpYlVUWj36O158vGzxVpRLk45PaHoxTvvzGIL2OGaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:45.957557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02682","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:923e625c3ce925e0dcbb34ab4043dbdca4a070f465974264e386600f06e2af9e","sha256:45a4bb68f1651c374837ae3bf95d9b73ce210b09eedc537a98b785b9527d2efd"],"state_sha256":"9f62e462219112cdaa971427c642e68d571ae70d11b4daf653808a7f241c19e8"}