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Our main result is a characterization of Schur multipliers in the case $1\\leq q \\leq p \\leq +\\infty$. When $1 < q \\leq p < +\\infty$, $\\phi \\in L^{\\infty}(\\Omega_1 \\times \\Omega_2)$ is a Schur multiplier on $\\mathcal{B}(L^p(\\Omega_1), L^q(\\Omega_2))$ if and only if there are a measur"},"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":"1703.08128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-23T16:17:27Z","cross_cats_sorted":[],"title_canon_sha256":"507eb504d4013ddfc1b088330c4e8712a00f5a860f21b099adf94b4fa3689f14","abstract_canon_sha256":"232dc6c32df5acbaa23eecac0050ed56ac57d75e5f3ddb92507d8a6ad5df97a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:03.801485Z","signature_b64":"SQU6U+Nz5x229bwnX91KIcUh+8tjtvLBJ+doGM6TMb3lwqE9cFAt03gOuEApsor09MBqSGelleIuyQUuljsJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b58104f122858229d4fbff31432c103c6d6b3e42714c2bbd32cb4f4cbc8916c4","last_reissued_at":"2026-05-18T00:48:03.800908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:03.800908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schur multipliers on $\\mathcal{B}(L^p,L^q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cl\\'ement Coine","submitted_at":"2017-03-23T16:17:27Z","abstract_excerpt":"Let $(\\Omega_1, \\mathcal{F}_1, \\mu_1)$ and $(\\Omega_2, \\mathcal{F}_2, \\mu_2)$ be two measure spaces and let $1 \\leq p,q \\leq +\\infty$. 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When $1 < q \\leq p < +\\infty$, $\\phi \\in L^{\\infty}(\\Omega_1 \\times \\Omega_2)$ is a Schur multiplier on $\\mathcal{B}(L^p(\\Omega_1), L^q(\\Omega_2))$ if and only if there are a measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08128","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":"1703.08128","created_at":"2026-05-18T00:48:03.801002+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.08128v1","created_at":"2026-05-18T00:48:03.801002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08128","created_at":"2026-05-18T00:48:03.801002+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWAQJ4JCQWBC","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWAQJ4JCQWBCTVH3","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWAQJ4JC","created_at":"2026-05-18T12:31:53.515858+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/WWAQJ4JCQWBCTVH374YUGLAQHR","json":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR.json","graph_json":"https://pith.science/api/pith-number/WWAQJ4JCQWBCTVH374YUGLAQHR/graph.json","events_json":"https://pith.science/api/pith-number/WWAQJ4JCQWBCTVH374YUGLAQHR/events.json","paper":"https://pith.science/paper/WWAQJ4JC"},"agent_actions":{"view_html":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR","download_json":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR.json","view_paper":"https://pith.science/paper/WWAQJ4JC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.08128&json=true","fetch_graph":"https://pith.science/api/pith-number/WWAQJ4JCQWBCTVH374YUGLAQHR/graph.json","fetch_events":"https://pith.science/api/pith-number/WWAQJ4JCQWBCTVH374YUGLAQHR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR/action/storage_attestation","attest_author":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR/action/author_attestation","sign_citation":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR/action/citation_signature","submit_replication":"https://pith.science/pith/WWAQJ4JCQWBCTVH374YUGLAQHR/action/replication_record"}},"created_at":"2026-05-18T00:48:03.801002+00:00","updated_at":"2026-05-18T00:48:03.801002+00:00"}