{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:2E3TBVNMI7YA2XTTDSXSWO2VUB","short_pith_number":"pith:2E3TBVNM","schema_version":"1.0","canonical_sha256":"d13730d5ac47f00d5e731caf2b3b55a04204b44e9b8d199a1764949ee4f7a308","source":{"kind":"arxiv","id":"math/0302326","version":1},"attestation_state":"computed","paper":{"title":"A unified approach to improved L^p Hardy inequalities with best constants","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"A. Tertikas, G. Barbatis, S. Filippas","submitted_at":"2003-02-26T15:10:46Z","abstract_excerpt":"We present a unified approach to improved $L^p$ Hardy inequalities in $\\R^N$. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where distance is taken from a surface of codimension $1<k<N$. In our main result we add to the right hand side of the classical Hardy inequality, a weighted $L^p$ norm with optimal weight and best constant. We also prove non-homogeneous improved Hardy inequalities, where the right hand side involves weighted L^q norms, q \\neq p."},"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":"math/0302326","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2003-02-26T15:10:46Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"b02f41961f528be663fd22dc47b0638c0ba8c91e60a31da88b5e1c150b93216e","abstract_canon_sha256":"81dafd6fa95c725f082a1b7953830e2101a9b7b9454ab77dff0a3166e062e0a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.069768Z","signature_b64":"SaVnSO2iMdLKXKjZgZOFpV0mr6XhBs4EuSEhglAkaj6I+Le61eKJ3q0ZjVd6E07BgkMOocMzpeqM8LgdvfUUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d13730d5ac47f00d5e731caf2b3b55a04204b44e9b8d199a1764949ee4f7a308","last_reissued_at":"2026-05-18T01:05:29.069351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.069351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A unified approach to improved L^p Hardy inequalities with best constants","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"A. Tertikas, G. Barbatis, S. Filippas","submitted_at":"2003-02-26T15:10:46Z","abstract_excerpt":"We present a unified approach to improved $L^p$ Hardy inequalities in $\\R^N$. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where distance is taken from a surface of codimension $1<k<N$. In our main result we add to the right hand side of the classical Hardy inequality, a weighted $L^p$ norm with optimal weight and best constant. We also prove non-homogeneous improved Hardy inequalities, where the right hand side involves weighted L^q norms, q \\neq p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302326","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":"math/0302326","created_at":"2026-05-18T01:05:29.069413+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0302326v1","created_at":"2026-05-18T01:05:29.069413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0302326","created_at":"2026-05-18T01:05:29.069413+00:00"},{"alias_kind":"pith_short_12","alias_value":"2E3TBVNMI7YA","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"2E3TBVNMI7YA2XTT","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"2E3TBVNM","created_at":"2026-05-18T12:25:51.375804+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/2E3TBVNMI7YA2XTTDSXSWO2VUB","json":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB.json","graph_json":"https://pith.science/api/pith-number/2E3TBVNMI7YA2XTTDSXSWO2VUB/graph.json","events_json":"https://pith.science/api/pith-number/2E3TBVNMI7YA2XTTDSXSWO2VUB/events.json","paper":"https://pith.science/paper/2E3TBVNM"},"agent_actions":{"view_html":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB","download_json":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB.json","view_paper":"https://pith.science/paper/2E3TBVNM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0302326&json=true","fetch_graph":"https://pith.science/api/pith-number/2E3TBVNMI7YA2XTTDSXSWO2VUB/graph.json","fetch_events":"https://pith.science/api/pith-number/2E3TBVNMI7YA2XTTDSXSWO2VUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB/action/storage_attestation","attest_author":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB/action/author_attestation","sign_citation":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB/action/citation_signature","submit_replication":"https://pith.science/pith/2E3TBVNMI7YA2XTTDSXSWO2VUB/action/replication_record"}},"created_at":"2026-05-18T01:05:29.069413+00:00","updated_at":"2026-05-18T01:05:29.069413+00:00"}