{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:AUOYQYBG3IHD7CPLLPXKZLVL5Q","short_pith_number":"pith:AUOYQYBG","schema_version":"1.0","canonical_sha256":"051d886026da0e3f89eb5beeacaeabec18a26655555b8f861e263096b545f06d","source":{"kind":"arxiv","id":"2310.19412","version":2},"attestation_state":"computed","paper":{"title":"Stein-Weiss inequality on non-compact symmetric spaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hong-Wei Zhang, Michael Ruzhansky, Vishvesh Kumar","submitted_at":"2023-10-30T10:23:16Z","abstract_excerpt":"Let $\\Delta$ be the Laplace-Beltrami operator on a non-compact symmetric space of any rank, and denote the bottom of its $L^2$-spectrum as $-|\\rho|^{2}$. In this paper, we provide a comprehensive characterization of both the sufficient and necessary conditions ensuring the validity of the Stein-Weiss inequality for the entire family of operators $\\lbrace{(-\\Delta+b)^{-\\frac{\\sigma}{2}}}\\rbrace_{\\sigma\\ge0,\\,b\\ge-|\\rho|^{2}}$. As an application, some weighted functional inequalities, such as Heisenberg's uncertainty principle, Gagliardo-Nirenberg's interpolation inequality, Pitt's inequality, e"},"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":"2310.19412","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2023-10-30T10:23:16Z","cross_cats_sorted":[],"title_canon_sha256":"a35b4f9b267af7708a535d6da71e056c6b8cc2abfa57a281cd684daaad7cd573","abstract_canon_sha256":"650a2e92be139c9e93536e9932f78aaf536a29a1435184cdc08228ef4363e590"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:07:19.237536Z","signature_b64":"NLFS7LDcZFZALg86OM8fKrOYkX0+QM7DQcHI7rHoR4+B36ogEE4IAF7l2Ys+KXQWa4mSL3COfQ3L/wwBnqYRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"051d886026da0e3f89eb5beeacaeabec18a26655555b8f861e263096b545f06d","last_reissued_at":"2026-07-05T07:07:19.237099Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:07:19.237099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stein-Weiss inequality on non-compact symmetric spaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hong-Wei Zhang, Michael Ruzhansky, Vishvesh Kumar","submitted_at":"2023-10-30T10:23:16Z","abstract_excerpt":"Let $\\Delta$ be the Laplace-Beltrami operator on a non-compact symmetric space of any rank, and denote the bottom of its $L^2$-spectrum as $-|\\rho|^{2}$. In this paper, we provide a comprehensive characterization of both the sufficient and necessary conditions ensuring the validity of the Stein-Weiss inequality for the entire family of operators $\\lbrace{(-\\Delta+b)^{-\\frac{\\sigma}{2}}}\\rbrace_{\\sigma\\ge0,\\,b\\ge-|\\rho|^{2}}$. As an application, some weighted functional inequalities, such as Heisenberg's uncertainty principle, Gagliardo-Nirenberg's interpolation inequality, Pitt's inequality, e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19412","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.19412/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2310.19412","created_at":"2026-07-05T07:07:19.237150+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.19412v2","created_at":"2026-07-05T07:07:19.237150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19412","created_at":"2026-07-05T07:07:19.237150+00:00"},{"alias_kind":"pith_short_12","alias_value":"AUOYQYBG3IHD","created_at":"2026-07-05T07:07:19.237150+00:00"},{"alias_kind":"pith_short_16","alias_value":"AUOYQYBG3IHD7CPL","created_at":"2026-07-05T07:07:19.237150+00:00"},{"alias_kind":"pith_short_8","alias_value":"AUOYQYBG","created_at":"2026-07-05T07:07:19.237150+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.22792","citing_title":"Shifted Pitt and uncertainty inequalities on Riemannian symmetric spaces of noncompact type","ref_index":50,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q","json":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q.json","graph_json":"https://pith.science/api/pith-number/AUOYQYBG3IHD7CPLLPXKZLVL5Q/graph.json","events_json":"https://pith.science/api/pith-number/AUOYQYBG3IHD7CPLLPXKZLVL5Q/events.json","paper":"https://pith.science/paper/AUOYQYBG"},"agent_actions":{"view_html":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q","download_json":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q.json","view_paper":"https://pith.science/paper/AUOYQYBG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.19412&json=true","fetch_graph":"https://pith.science/api/pith-number/AUOYQYBG3IHD7CPLLPXKZLVL5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/AUOYQYBG3IHD7CPLLPXKZLVL5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q/action/storage_attestation","attest_author":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q/action/author_attestation","sign_citation":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q/action/citation_signature","submit_replication":"https://pith.science/pith/AUOYQYBG3IHD7CPLLPXKZLVL5Q/action/replication_record"}},"created_at":"2026-07-05T07:07:19.237150+00:00","updated_at":"2026-07-05T07:07:19.237150+00:00"}