{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Q7CMKFYU3KWEJXGDXAGMOJEMBL","short_pith_number":"pith:Q7CMKFYU","schema_version":"1.0","canonical_sha256":"87c4c51714daac44dcc3b80cc7248c0ae3ac838224ad4f4b0b1a7a944a6a690c","source":{"kind":"arxiv","id":"1309.5839","version":3},"attestation_state":"computed","paper":{"title":"Two weight norm inequalities for the $g$ function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kangwei Li, Michael T Lacey","submitted_at":"2013-09-23T15:20:09Z","abstract_excerpt":"Given two weights $\\sigma, w$ on $\\mathbb R ^{n}$, the classical $g$-function satisfies the norm inequality $\\lVert g (f\\sigma)\\rVert_{L ^2 (w)} \\lesssim \\lVert f\\rVert_{L ^2 (\\sigma)}$ if and only if the two weight Muckenhoupt $A_2$ condition holds, and a family of testing conditions holds, namely \\begin{equation*} \\iint_{Q (I)} (\\nabla P_t (\\sigma \\mathbf 1_I)(x, t))^2 \\; dw \\, t dt \\lesssim \\sigma (I) \\end{equation*} uniformly over all cubes $I \\subset \\mathbb R ^{n}$, and $Q (I)$ is the Carleson box over $I$. A corresponding characterization for the intrinsic square function of Wilson also"},"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":"1309.5839","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-23T15:20:09Z","cross_cats_sorted":[],"title_canon_sha256":"0300a176c224fe9fcb556beb0c5a78c1edbb9dd44d2af1289a7c13e5127b98e8","abstract_canon_sha256":"6c0402e7b891b215fc5d26d12ec2ef274a4bf67019a0e6395e497b6ae1a0c2ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:10.043254Z","signature_b64":"AZqhxw8ArGGExcf0J94fuVvaLD1C/CdXxqdx/W7/3Bx5ykck0q8s6EGWHDK8qaPoReLqeoiHEAUxtrZCjZrcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87c4c51714daac44dcc3b80cc7248c0ae3ac838224ad4f4b0b1a7a944a6a690c","last_reissued_at":"2026-05-18T01:13:10.042844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:10.042844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two weight norm inequalities for the $g$ function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kangwei Li, Michael T Lacey","submitted_at":"2013-09-23T15:20:09Z","abstract_excerpt":"Given two weights $\\sigma, w$ on $\\mathbb R ^{n}$, the classical $g$-function satisfies the norm inequality $\\lVert g (f\\sigma)\\rVert_{L ^2 (w)} \\lesssim \\lVert f\\rVert_{L ^2 (\\sigma)}$ if and only if the two weight Muckenhoupt $A_2$ condition holds, and a family of testing conditions holds, namely \\begin{equation*} \\iint_{Q (I)} (\\nabla P_t (\\sigma \\mathbf 1_I)(x, t))^2 \\; dw \\, t dt \\lesssim \\sigma (I) \\end{equation*} uniformly over all cubes $I \\subset \\mathbb R ^{n}$, and $Q (I)$ is the Carleson box over $I$. A corresponding characterization for the intrinsic square function of Wilson also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5839","kind":"arxiv","version":3},"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":"1309.5839","created_at":"2026-05-18T01:13:10.042899+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.5839v3","created_at":"2026-05-18T01:13:10.042899+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5839","created_at":"2026-05-18T01:13:10.042899+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q7CMKFYU3KWE","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q7CMKFYU3KWEJXGD","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q7CMKFYU","created_at":"2026-05-18T12:27:57.521954+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/Q7CMKFYU3KWEJXGDXAGMOJEMBL","json":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL.json","graph_json":"https://pith.science/api/pith-number/Q7CMKFYU3KWEJXGDXAGMOJEMBL/graph.json","events_json":"https://pith.science/api/pith-number/Q7CMKFYU3KWEJXGDXAGMOJEMBL/events.json","paper":"https://pith.science/paper/Q7CMKFYU"},"agent_actions":{"view_html":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL","download_json":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL.json","view_paper":"https://pith.science/paper/Q7CMKFYU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.5839&json=true","fetch_graph":"https://pith.science/api/pith-number/Q7CMKFYU3KWEJXGDXAGMOJEMBL/graph.json","fetch_events":"https://pith.science/api/pith-number/Q7CMKFYU3KWEJXGDXAGMOJEMBL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL/action/storage_attestation","attest_author":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL/action/author_attestation","sign_citation":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL/action/citation_signature","submit_replication":"https://pith.science/pith/Q7CMKFYU3KWEJXGDXAGMOJEMBL/action/replication_record"}},"created_at":"2026-05-18T01:13:10.042899+00:00","updated_at":"2026-05-18T01:13:10.042899+00:00"}