{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WSSS5NSAKGAMK7UUYBUVCF6LQR","short_pith_number":"pith:WSSS5NSA","schema_version":"1.0","canonical_sha256":"b4a52eb6405180c57e94c0695117cb844cecd9adc750141d9e863af6548b5cde","source":{"kind":"arxiv","id":"1906.07999","version":1},"attestation_state":"computed","paper":{"title":"Discrete Harmonic Analysis associated with Jacobi expansions III: the Littlewood-Paley-Stein $g_{k}$-functions and the Laplace type multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Arenas, Edgar Labarga, \\'Oscar Ciaurri","submitted_at":"2019-06-19T09:44:06Z","abstract_excerpt":"The research about Harmonic Analysis associated with Jacobi expansions carried out in \\cite{ACL-JacI} and \\cite{ACL-JacII} is continued in this paper. Given the operator $\\mathcal{J}^{(\\alpha,\\beta)}=J^{(\\alpha,\\beta)}-I$, where $J^{(\\alpha,\\beta)}$ is the three-term recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator, we define the corresponding Littlewood-Paley-Stein $g_k^{(\\alpha,\\beta)}$-functions associated with it and we prove an equivalence of norms with weights for them. As a consequence, we deduce a result for Laplace type multipliers."},"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":"1906.07999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-19T09:44:06Z","cross_cats_sorted":[],"title_canon_sha256":"5d34e764ee82ddaab68a4a477e27ede28c98e114b4a67bed935fe801e78a392e","abstract_canon_sha256":"7e4e9d61e51c280e20288b4da889c45f2bcbc013401e6cb1e35e48d0bf4b1f40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:54.939878Z","signature_b64":"6Bh4+EV/D6VSngE8MLn2QhHDIdv+JyPghP5jCG0mLvuOHMrfEMWPDddGG3qvhKzrlI3zV0nDByvfzaLfpBRPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4a52eb6405180c57e94c0695117cb844cecd9adc750141d9e863af6548b5cde","last_reissued_at":"2026-05-17T23:42:54.939176Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:54.939176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete Harmonic Analysis associated with Jacobi expansions III: the Littlewood-Paley-Stein $g_{k}$-functions and the Laplace type multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Arenas, Edgar Labarga, \\'Oscar Ciaurri","submitted_at":"2019-06-19T09:44:06Z","abstract_excerpt":"The research about Harmonic Analysis associated with Jacobi expansions carried out in \\cite{ACL-JacI} and \\cite{ACL-JacII} is continued in this paper. Given the operator $\\mathcal{J}^{(\\alpha,\\beta)}=J^{(\\alpha,\\beta)}-I$, where $J^{(\\alpha,\\beta)}$ is the three-term recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator, we define the corresponding Littlewood-Paley-Stein $g_k^{(\\alpha,\\beta)}$-functions associated with it and we prove an equivalence of norms with weights for them. As a consequence, we deduce a result for Laplace type multipliers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07999","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":"1906.07999","created_at":"2026-05-17T23:42:54.939274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.07999v1","created_at":"2026-05-17T23:42:54.939274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07999","created_at":"2026-05-17T23:42:54.939274+00:00"},{"alias_kind":"pith_short_12","alias_value":"WSSS5NSAKGAM","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"WSSS5NSAKGAMK7UU","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"WSSS5NSA","created_at":"2026-05-18T12:33:30.264802+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/WSSS5NSAKGAMK7UUYBUVCF6LQR","json":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR.json","graph_json":"https://pith.science/api/pith-number/WSSS5NSAKGAMK7UUYBUVCF6LQR/graph.json","events_json":"https://pith.science/api/pith-number/WSSS5NSAKGAMK7UUYBUVCF6LQR/events.json","paper":"https://pith.science/paper/WSSS5NSA"},"agent_actions":{"view_html":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR","download_json":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR.json","view_paper":"https://pith.science/paper/WSSS5NSA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.07999&json=true","fetch_graph":"https://pith.science/api/pith-number/WSSS5NSAKGAMK7UUYBUVCF6LQR/graph.json","fetch_events":"https://pith.science/api/pith-number/WSSS5NSAKGAMK7UUYBUVCF6LQR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR/action/storage_attestation","attest_author":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR/action/author_attestation","sign_citation":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR/action/citation_signature","submit_replication":"https://pith.science/pith/WSSS5NSAKGAMK7UUYBUVCF6LQR/action/replication_record"}},"created_at":"2026-05-17T23:42:54.939274+00:00","updated_at":"2026-05-17T23:42:54.939274+00:00"}