{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E3TEVE2CQO34U7XOKXRGRMLGF7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"495532ead04fcb640f03943ca1464fc77b10e778761e0fd2848f17d5078421da","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-27T13:41:19Z","title_canon_sha256":"914940927dd3cd9d7ae85f3e63a68b50f46ca6e1752ebf2d93d955eb5958ce33"},"schema_version":"1.0","source":{"id":"1308.5869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5869","created_at":"2026-05-18T01:47:57Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5869v1","created_at":"2026-05-18T01:47:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5869","created_at":"2026-05-18T01:47:57Z"},{"alias_kind":"pith_short_12","alias_value":"E3TEVE2CQO34","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E3TEVE2CQO34U7XO","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E3TEVE2C","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:365dd28b5c028c8a60704d5cc922f74c7ee19df1386d053375c3d08f6c50ed27","target":"graph","created_at":"2026-05-18T01:47:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $({\\mathcal X},\\,d,\\,\\mu)$ be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of T. Hyt\\\"onen. In this paper, the authors prove that the $L^p(\\mu)$ boundedness with $p\\in(1,\\,\\infty)$ of the Marcinkiewicz integral is equivalent to either of its boundedness from $L^1(\\mu)$ into $L^{1,\\infty}(\\mu)$ or from the atomic Hardy space $H^1(\\mu)$ into $L^1(\\mu)$. Moreover, the authors show that, if the Marcinkiewicz integral is bounded from $H^1(\\mu)$ into $L^1(\\mu)$, then it is also bounded from $L^\\infty(\\mu)$ into the space ${\\","authors_text":"Dachun Yang, Haibo Lin","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-27T13:41:19Z","title":"Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5869","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5d246b4449340dd6fd91d8a172267f3081d1fb760b542aaeb9866eb45e6ef50a","target":"record","created_at":"2026-05-18T01:47:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"495532ead04fcb640f03943ca1464fc77b10e778761e0fd2848f17d5078421da","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-27T13:41:19Z","title_canon_sha256":"914940927dd3cd9d7ae85f3e63a68b50f46ca6e1752ebf2d93d955eb5958ce33"},"schema_version":"1.0","source":{"id":"1308.5869","kind":"arxiv","version":1}},"canonical_sha256":"26e64a934283b7ca7eee55e268b1662fe2cee634be32b4615ef7b3c6c8ec8991","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26e64a934283b7ca7eee55e268b1662fe2cee634be32b4615ef7b3c6c8ec8991","first_computed_at":"2026-05-18T01:47:57.978433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:57.978433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O97ucWnZGubagEbg5F5mfwZkOT4YKjHjKuQxfrViOVTfysogX2gQrxlAIERb3D2ixfxfhIGOKSw0VCQIITahBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:57.979053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d246b4449340dd6fd91d8a172267f3081d1fb760b542aaeb9866eb45e6ef50a","sha256:365dd28b5c028c8a60704d5cc922f74c7ee19df1386d053375c3d08f6c50ed27"],"state_sha256":"e7e96e51fd79857b5de885adbc4aece1e6be7e5a050f1c809fe4add5cbdc563f"}