{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:45UNN7Z6VWZG6554IXHPLTPW7D","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":"ed3e74b5e297f32569a6fe976f655ff3408607ac89937331764df68725f5c4b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-09T17:48:46Z","title_canon_sha256":"e2e5209233e7467aa1a4a772d3c69e1f8f8b2fc9c4d6b4d533c188df98d6e3eb"},"schema_version":"1.0","source":{"id":"1202.2063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2063","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2063v2","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2063","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"45UNN7Z6VWZG","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"45UNN7Z6VWZG6554","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"45UNN7Z6","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:e7d1ccae85c689611ff54fb750d127ba1c1102614bd63d8b98bd708305c7b855","target":"graph","created_at":"2026-05-18T03:44:36Z","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 $(X, d, \\mu)$ be a space of homogeneous type, i.e. the measure $\\mu$ satisfies doubling (volume) property with respect to the balls defined by the metric $d$. Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that the semigroup of $L$ satisfies the Davies-Gaffney estimates. In this paper, we study the weighted Hardy spaces $H^p_{L,w}(X)$, $0 < p \\le 1$, associated to the operator $L$ on the space $X$. We establish the atomic and the molecular characterizations of elements in $H^p_{L,w}(X)$. As applications, we obtain the boundedness on $\\HL$ for the generalized Riesz tran","authors_text":"The Anh Bui, Xuan Thinh Duong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-09T17:48:46Z","title":"Weighted Hardy spaces associated to operators and boundedness of singular integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2063","kind":"arxiv","version":2},"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":"sha256:69ff8218258dfb0d91823ee20d1520546ea5c7507a8ab9b366a9f5ab2d717f2c","target":"record","created_at":"2026-05-18T03:44:36Z","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":"ed3e74b5e297f32569a6fe976f655ff3408607ac89937331764df68725f5c4b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-09T17:48:46Z","title_canon_sha256":"e2e5209233e7467aa1a4a772d3c69e1f8f8b2fc9c4d6b4d533c188df98d6e3eb"},"schema_version":"1.0","source":{"id":"1202.2063","kind":"arxiv","version":2}},"canonical_sha256":"e768d6ff3eadb26f77bc45cef5cdf6f8f2c8a3524ce9227ce98e5cc1fff79271","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e768d6ff3eadb26f77bc45cef5cdf6f8f2c8a3524ce9227ce98e5cc1fff79271","first_computed_at":"2026-05-18T03:44:36.078643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:36.078643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7GPwIf8eYvQyEY72PDAA14Li2fm/tfOBjg2FMWXtooAb7CWGj8zqCAtzeP+DKas6086LOmX5Mp0JEIj4UipOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:36.079373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69ff8218258dfb0d91823ee20d1520546ea5c7507a8ab9b366a9f5ab2d717f2c","sha256:e7d1ccae85c689611ff54fb750d127ba1c1102614bd63d8b98bd708305c7b855"],"state_sha256":"4451666b3d2951912e18b27574c84cc9b4dadc9c8581799fbb1e2a6cbc173984"}