{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BOTGE3TVMPVCK6GQNMWLL66E3Y","short_pith_number":"pith:BOTGE3TV","schema_version":"1.0","canonical_sha256":"0ba6626e7563ea2578d06b2cb5fbc4de0b92e06fd64dae460c653efb8fc317d2","source":{"kind":"arxiv","id":"1309.6512","version":1},"attestation_state":"computed","paper":{"title":"Boundedness of Intrinsic Littlewood-Paley Functions on Musielak-Orlicz Morrey and Campanato Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Eiichi Nakai, Junqiang Zhang, Yiyu Liang","submitted_at":"2013-09-25T14:13:10Z","abstract_excerpt":"Let $\\varphi: {\\mathbb R^n}\\times [0,\\infty)\\to[0,\\infty)$ be such that $\\vz(x,\\cdot)$ is nondecreasing, $\\varphi(x,0)=0$, $\\varphi(x,t)>0$ when $t>0$, $\\lim_{t\\to\\infty}\\varphi(x,t)=\\infty$ and $\\vz(\\cdot,t)$ is a Muckenhoupt $A_\\infty({\\mathbb R^n})$ weight uniformly in $t$. Let $\\phi: [0,\\infty)\\to[0,\\infty)$ be nondecreasing. In this article, the authors introduce the Musielak-Orlicz Morrey space $\\mathcal M^{\\varphi,\\phi}(\\mathbb R^n)$ and obtain the boundedness on $\\mathcal M^{\\varphi,\\phi}(\\mathbb R^n)$ of the intrinsic Lusin area function $S_{\\alpha}$, the intrinsic $g$-function $g_{\\a"},"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":"1309.6512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-25T14:13:10Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"e2f2e42f1387727b3ce3dc72b005bcdddd91ddbfb3e77e3c537682de0b6b340f","abstract_canon_sha256":"8e4b2d6eb3e66c9e15da6cb849bdbc07af14952e71047706097e9d78380501af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:20.790808Z","signature_b64":"ArFNSdJBsF0RJWWqz9+yToly0mGgM7OE58G8x4uup9hIBF/P751jPs3hUefl1WGg78kyGatAwEkQ9o6hxj1bCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ba6626e7563ea2578d06b2cb5fbc4de0b92e06fd64dae460c653efb8fc317d2","last_reissued_at":"2026-05-18T03:12:20.789947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:20.789947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundedness of Intrinsic Littlewood-Paley Functions on Musielak-Orlicz Morrey and Campanato Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Eiichi Nakai, Junqiang Zhang, Yiyu Liang","submitted_at":"2013-09-25T14:13:10Z","abstract_excerpt":"Let $\\varphi: {\\mathbb R^n}\\times [0,\\infty)\\to[0,\\infty)$ be such that $\\vz(x,\\cdot)$ is nondecreasing, $\\varphi(x,0)=0$, $\\varphi(x,t)>0$ when $t>0$, $\\lim_{t\\to\\infty}\\varphi(x,t)=\\infty$ and $\\vz(\\cdot,t)$ is a Muckenhoupt $A_\\infty({\\mathbb R^n})$ weight uniformly in $t$. Let $\\phi: [0,\\infty)\\to[0,\\infty)$ be nondecreasing. In this article, the authors introduce the Musielak-Orlicz Morrey space $\\mathcal M^{\\varphi,\\phi}(\\mathbb R^n)$ and obtain the boundedness on $\\mathcal M^{\\varphi,\\phi}(\\mathbb R^n)$ of the intrinsic Lusin area function $S_{\\alpha}$, the intrinsic $g$-function $g_{\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6512","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":"1309.6512","created_at":"2026-05-18T03:12:20.790102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6512v1","created_at":"2026-05-18T03:12:20.790102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6512","created_at":"2026-05-18T03:12:20.790102+00:00"},{"alias_kind":"pith_short_12","alias_value":"BOTGE3TVMPVC","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BOTGE3TVMPVCK6GQ","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BOTGE3TV","created_at":"2026-05-18T12:27:40.988391+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/BOTGE3TVMPVCK6GQNMWLL66E3Y","json":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y.json","graph_json":"https://pith.science/api/pith-number/BOTGE3TVMPVCK6GQNMWLL66E3Y/graph.json","events_json":"https://pith.science/api/pith-number/BOTGE3TVMPVCK6GQNMWLL66E3Y/events.json","paper":"https://pith.science/paper/BOTGE3TV"},"agent_actions":{"view_html":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y","download_json":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y.json","view_paper":"https://pith.science/paper/BOTGE3TV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6512&json=true","fetch_graph":"https://pith.science/api/pith-number/BOTGE3TVMPVCK6GQNMWLL66E3Y/graph.json","fetch_events":"https://pith.science/api/pith-number/BOTGE3TVMPVCK6GQNMWLL66E3Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y/action/storage_attestation","attest_author":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y/action/author_attestation","sign_citation":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y/action/citation_signature","submit_replication":"https://pith.science/pith/BOTGE3TVMPVCK6GQNMWLL66E3Y/action/replication_record"}},"created_at":"2026-05-18T03:12:20.790102+00:00","updated_at":"2026-05-18T03:12:20.790102+00:00"}