{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ABAFFS765JKPSMNWE4TKJCL3QH","short_pith_number":"pith:ABAFFS76","schema_version":"1.0","canonical_sha256":"004052cbfeea54f931b62726a4897b81e27916f0123eaf0707a28615d0403bcd","source":{"kind":"arxiv","id":"1306.1437","version":4},"attestation_state":"computed","paper":{"title":"On the continuity of Fourier multipliers on the homogeneous Sobolev spaces $\\dot{W}^1_1(R^d)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Krystian Kazaniecki, Micha{\\l} Wojciechowski","submitted_at":"2013-06-06T15:28:44Z","abstract_excerpt":"In this paper we proof that every Fourier multiplier on homogeneous sobolev space $\\dot{W}_1^1(\\mathbb{R}^d)$ is a continuous function. Our theorem is generalization of A. Bonami and S. Poornima result for Fourier multipliers, which are homogeneous functions of degree zero."},"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":"1306.1437","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-06T15:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"293aa0499764938ffc32aecb73ac557d254742ebe6720958748343d7bed621dd","abstract_canon_sha256":"bffd8fbb049a6b4549c73f919569320564fbb32ba80cef187882c606c6f82fdf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:24.931137Z","signature_b64":"XBpeEFThs4A1VUE3ORKUByTFQBmW2xS5KfJX5U/8E0x7QjDhq57+TKWJHcTHko9MTxMx/CwRtE3PXq/uyb+KBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"004052cbfeea54f931b62726a4897b81e27916f0123eaf0707a28615d0403bcd","last_reissued_at":"2026-05-17T23:52:24.930445Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:24.930445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the continuity of Fourier multipliers on the homogeneous Sobolev spaces $\\dot{W}^1_1(R^d)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Krystian Kazaniecki, Micha{\\l} Wojciechowski","submitted_at":"2013-06-06T15:28:44Z","abstract_excerpt":"In this paper we proof that every Fourier multiplier on homogeneous sobolev space $\\dot{W}_1^1(\\mathbb{R}^d)$ is a continuous function. Our theorem is generalization of A. Bonami and S. Poornima result for Fourier multipliers, which are homogeneous functions of degree zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1437","kind":"arxiv","version":4},"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":"1306.1437","created_at":"2026-05-17T23:52:24.930559+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.1437v4","created_at":"2026-05-17T23:52:24.930559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1437","created_at":"2026-05-17T23:52:24.930559+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABAFFS765JKP","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABAFFS765JKPSMNW","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABAFFS76","created_at":"2026-05-18T12:27:38.830355+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/ABAFFS765JKPSMNWE4TKJCL3QH","json":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH.json","graph_json":"https://pith.science/api/pith-number/ABAFFS765JKPSMNWE4TKJCL3QH/graph.json","events_json":"https://pith.science/api/pith-number/ABAFFS765JKPSMNWE4TKJCL3QH/events.json","paper":"https://pith.science/paper/ABAFFS76"},"agent_actions":{"view_html":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH","download_json":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH.json","view_paper":"https://pith.science/paper/ABAFFS76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.1437&json=true","fetch_graph":"https://pith.science/api/pith-number/ABAFFS765JKPSMNWE4TKJCL3QH/graph.json","fetch_events":"https://pith.science/api/pith-number/ABAFFS765JKPSMNWE4TKJCL3QH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH/action/storage_attestation","attest_author":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH/action/author_attestation","sign_citation":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH/action/citation_signature","submit_replication":"https://pith.science/pith/ABAFFS765JKPSMNWE4TKJCL3QH/action/replication_record"}},"created_at":"2026-05-17T23:52:24.930559+00:00","updated_at":"2026-05-17T23:52:24.930559+00:00"}