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Namely, we construct a function $f\\in B\\_{p,q}^s(\\mathbb{R}^N)$ such that $f(\\cdot,y)\\notin B\\_{p,q}^s(\\mathbb{R}^d)$ for a.e. $y\\in \\mathbb{R}^{N-d}$. We show that, in fact, $f(\\cdot,y)$ belong to $B\\_{p,q}^{(s,\\Psi)}(\\mathbb{R}^d)$ for a.e. $y\\in\\mathbb{R}^{N-d}$, a Besov space of generalized smoothness, and, when $q"},"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":"1706.04462","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-14T13:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"4699007016ce8f2877bc3210ab4f3331faa3508df2f6bcac6d9b8e2e292edb96","abstract_canon_sha256":"8b368a3152db42d610c7317b8cf90a76664da5d235afe25e01975e0e7f3a8ace"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:16.341238Z","signature_b64":"OQSv1typ8tRUIOpWL26P6ub1guG9Fr9sAR5nOGhnwcfn+RbZZdPzEwBf5hEdbwVWlfXIzWEqdOn5mbsgcbRhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1578484cd4b96c2ce796bf5106312ea0d054387d28499cb430f4b4311a11c9dd","last_reissued_at":"2026-05-18T00:26:16.340754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:16.340754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On restrictions of Besov functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Julien Brasseur (I2M)","submitted_at":"2017-06-14T13:01:35Z","abstract_excerpt":"In this paper, we study the smoothness of restrictions of Besov functions. It is known that for any $f\\in B\\_{p,q}^s(\\mathbb{R}^N)$ with $q\\leq p$ we have $f(\\cdot,y)\\in B\\_{p,q}^s(\\mathbb{R}^d)$ for a.e. $y\\in \\mathbb{R}^{N-d}$. We prove that this is no longer true when $p\\<q$. Namely, we construct a function $f\\in B\\_{p,q}^s(\\mathbb{R}^N)$ such that $f(\\cdot,y)\\notin B\\_{p,q}^s(\\mathbb{R}^d)$ for a.e. $y\\in \\mathbb{R}^{N-d}$. We show that, in fact, $f(\\cdot,y)$ belong to $B\\_{p,q}^{(s,\\Psi)}(\\mathbb{R}^d)$ for a.e. $y\\in\\mathbb{R}^{N-d}$, a Besov space of generalized smoothness, and, when $q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04462","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":"1706.04462","created_at":"2026-05-18T00:26:16.340835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.04462v2","created_at":"2026-05-18T00:26:16.340835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04462","created_at":"2026-05-18T00:26:16.340835+00:00"},{"alias_kind":"pith_short_12","alias_value":"CV4EQTGUXFWC","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CV4EQTGUXFWCZZ4W","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CV4EQTGU","created_at":"2026-05-18T12:31:10.602751+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/CV4EQTGUXFWCZZ4WX5IQMMJOUD","json":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD.json","graph_json":"https://pith.science/api/pith-number/CV4EQTGUXFWCZZ4WX5IQMMJOUD/graph.json","events_json":"https://pith.science/api/pith-number/CV4EQTGUXFWCZZ4WX5IQMMJOUD/events.json","paper":"https://pith.science/paper/CV4EQTGU"},"agent_actions":{"view_html":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD","download_json":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD.json","view_paper":"https://pith.science/paper/CV4EQTGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.04462&json=true","fetch_graph":"https://pith.science/api/pith-number/CV4EQTGUXFWCZZ4WX5IQMMJOUD/graph.json","fetch_events":"https://pith.science/api/pith-number/CV4EQTGUXFWCZZ4WX5IQMMJOUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD/action/storage_attestation","attest_author":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD/action/author_attestation","sign_citation":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD/action/citation_signature","submit_replication":"https://pith.science/pith/CV4EQTGUXFWCZZ4WX5IQMMJOUD/action/replication_record"}},"created_at":"2026-05-18T00:26:16.340835+00:00","updated_at":"2026-05-18T00:26:16.340835+00:00"}