{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:V2KUWAK6L7QMPBRJYPHFDOEUIB","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":"56e5c4f2156042245978a89a6cdfd0927f912352b49cc24efc770cbf958a3a4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-12T18:07:26Z","title_canon_sha256":"d4443bfae0b3089a4287f41f98d382ee6209cdd414b0ac7d79980e1edb222274"},"schema_version":"1.0","source":{"id":"1902.04527","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04527","created_at":"2026-07-05T00:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04527v6","created_at":"2026-07-05T00:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04527","created_at":"2026-07-05T00:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"V2KUWAK6L7QM","created_at":"2026-07-05T00:58:02Z"},{"alias_kind":"pith_short_16","alias_value":"V2KUWAK6L7QMPBRJ","created_at":"2026-07-05T00:58:02Z"},{"alias_kind":"pith_short_8","alias_value":"V2KUWAK6","created_at":"2026-07-05T00:58:02Z"}],"graph_snapshots":[{"event_id":"sha256:5ad95323cf19b2163f6af2fd45ffcb9ad0120e4e3158eec21c55a5f591e83497","target":"graph","created_at":"2026-07-05T00:58:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.04527/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In [C. E. Kenig and E. M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett., 6(1):1-15, 1999], the following type of multilinear fractional integral \\[\n  \\int_{\\mathbb{R}^{mn}} \\frac{f_1(l_1(x_1,\\ldots,x_m,x))\\cdots f_{m+1}(l_{m+1}(x_1,\\ldots,x_m,x))}{(|x_1|+\\ldots+|x_m|)^{\\lambda}} dx_1\\ldots dx_m \\] was studied, where $l_i$ are linear maps from $\\mathbb{R}^{(m+1)n}$ to $\\mathbb{R}^n$ satisfying certain conditions. They proved the boundedness of such multilinear fractional integral from $L^{p_1}\\times \\ldots \\times L^{p_{m+1}}$ to $L^q$ when the indices satisfy the hom","authors_text":"Ting Chen, Wenchang Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-12T18:07:26Z","title":"Extension of Multilinear Fractional Integral Operators to Linear Operators on Lebesgue Spaces with Mixed Norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04527","kind":"arxiv","version":6},"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:bfb56bc5deed3cdc224452a937860105fc68ecafb41bad32fc588732ab77f6eb","target":"record","created_at":"2026-07-05T00:58:02Z","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":"56e5c4f2156042245978a89a6cdfd0927f912352b49cc24efc770cbf958a3a4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-12T18:07:26Z","title_canon_sha256":"d4443bfae0b3089a4287f41f98d382ee6209cdd414b0ac7d79980e1edb222274"},"schema_version":"1.0","source":{"id":"1902.04527","kind":"arxiv","version":6}},"canonical_sha256":"ae954b015e5fe0c78629c3ce51b89440488f77e543dca1a4a3753cf0ed9899e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae954b015e5fe0c78629c3ce51b89440488f77e543dca1a4a3753cf0ed9899e7","first_computed_at":"2026-07-05T00:58:02.072140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:58:02.072140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZjDdb2bZadVisw/l9W1FaIfrZHRBufRKnWHJAsK/3n1UeANuntmark/IG9NFCR8EZm3jtrAD0gI2Q07MicQbAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:58:02.072648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.04527","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfb56bc5deed3cdc224452a937860105fc68ecafb41bad32fc588732ab77f6eb","sha256:5ad95323cf19b2163f6af2fd45ffcb9ad0120e4e3158eec21c55a5f591e83497"],"state_sha256":"fc5b8106da71a2389b8fe2eea9df6efef975fd02846422d83953772fef6384d4"}