{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SFQ4B3ZIILEFN5K3EZYJZNL7JW","short_pith_number":"pith:SFQ4B3ZI","schema_version":"1.0","canonical_sha256":"9161c0ef2842c856f55b26709cb57f4da626273fd749de772cab6bf5bbe09aa9","source":{"kind":"arxiv","id":"1405.6045","version":2},"attestation_state":"computed","paper":{"title":"Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fatih Deringoz, Vagif S. Guliyev","submitted_at":"2014-05-23T12:44:25Z","abstract_excerpt":"We consider generalized Orlicz-Morrey spaces $M_{\\Phi,\\varphi}(\\mathbb{R}^{n})$ including their weak versions $WM_{\\Phi,\\varphi}(\\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(\\varphi_{1},\\varphi_{2})$ and $(\\Phi, \\Psi)$ which ensures the boundedness of the fractional maximal operator $M_{\\alpha}$ from $M_{\\Phi,\\varphi_1}(\\mathbb{R}^{n})$ to $M_{\\Psi,\\varphi_2}(\\mathbb{R}^{n})$ and from $M_{\\Phi,\\varphi_1}(\\mathbb{R}^{n})$ to $WM_{\\Psi,\\varphi_2}(\\mathbb{R}^{n})$. As applications of those results, the boundedness of the commutators of the fractional maximal operator $M_{b,\\"},"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":"1405.6045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-23T12:44:25Z","cross_cats_sorted":[],"title_canon_sha256":"8472b0f1b00bd6243e65a2c8630f6d4cb518496d76b8dd2f048a52cde8cf2435","abstract_canon_sha256":"a7b8482a6083ec2d41309ce9550b9e4b56e6ad7d62e4f603c2b1f75ae88db9ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:23.690787Z","signature_b64":"QJK7J9dcx1ePbF5JyKG2+8tF3l24UzRBtjuYrPU4Yj8efx1rfhX1J3pRMJszhqKsq1Ug8+IDGedFIzF1znGGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9161c0ef2842c856f55b26709cb57f4da626273fd749de772cab6bf5bbe09aa9","last_reissued_at":"2026-05-18T02:39:23.690447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:23.690447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fatih Deringoz, Vagif S. Guliyev","submitted_at":"2014-05-23T12:44:25Z","abstract_excerpt":"We consider generalized Orlicz-Morrey spaces $M_{\\Phi,\\varphi}(\\mathbb{R}^{n})$ including their weak versions $WM_{\\Phi,\\varphi}(\\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(\\varphi_{1},\\varphi_{2})$ and $(\\Phi, \\Psi)$ which ensures the boundedness of the fractional maximal operator $M_{\\alpha}$ from $M_{\\Phi,\\varphi_1}(\\mathbb{R}^{n})$ to $M_{\\Psi,\\varphi_2}(\\mathbb{R}^{n})$ and from $M_{\\Phi,\\varphi_1}(\\mathbb{R}^{n})$ to $WM_{\\Psi,\\varphi_2}(\\mathbb{R}^{n})$. As applications of those results, the boundedness of the commutators of the fractional maximal operator $M_{b,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6045","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":"1405.6045","created_at":"2026-05-18T02:39:23.690502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6045v2","created_at":"2026-05-18T02:39:23.690502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6045","created_at":"2026-05-18T02:39:23.690502+00:00"},{"alias_kind":"pith_short_12","alias_value":"SFQ4B3ZIILEF","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SFQ4B3ZIILEFN5K3","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SFQ4B3ZI","created_at":"2026-05-18T12:28:49.207871+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/SFQ4B3ZIILEFN5K3EZYJZNL7JW","json":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW.json","graph_json":"https://pith.science/api/pith-number/SFQ4B3ZIILEFN5K3EZYJZNL7JW/graph.json","events_json":"https://pith.science/api/pith-number/SFQ4B3ZIILEFN5K3EZYJZNL7JW/events.json","paper":"https://pith.science/paper/SFQ4B3ZI"},"agent_actions":{"view_html":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW","download_json":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW.json","view_paper":"https://pith.science/paper/SFQ4B3ZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6045&json=true","fetch_graph":"https://pith.science/api/pith-number/SFQ4B3ZIILEFN5K3EZYJZNL7JW/graph.json","fetch_events":"https://pith.science/api/pith-number/SFQ4B3ZIILEFN5K3EZYJZNL7JW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW/action/storage_attestation","attest_author":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW/action/author_attestation","sign_citation":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW/action/citation_signature","submit_replication":"https://pith.science/pith/SFQ4B3ZIILEFN5K3EZYJZNL7JW/action/replication_record"}},"created_at":"2026-05-18T02:39:23.690502+00:00","updated_at":"2026-05-18T02:39:23.690502+00:00"}