{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LJOVGSSXOMRKHSHFVMGCVYLLMX","short_pith_number":"pith:LJOVGSSX","schema_version":"1.0","canonical_sha256":"5a5d534a577322a3c8e5ab0c2ae16b65cc0325c203fce4d56cb9db75719b8469","source":{"kind":"arxiv","id":"1105.2661","version":8},"attestation_state":"computed","paper":{"title":"Two-weight norm inequalities for potential type and maximal operators in a metric space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Anna Kairema","submitted_at":"2011-05-13T08:45:14Z","abstract_excerpt":"We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty annulus property, which appeared in earlier works on the subject. One of the new ingredients in the proof is the use of a finite collection of adjacent dyadic systems recently constructed by the author and T. Hyt\\\"onen. We further extend the previous Euclidean characterization of two-weight norm inequalities for fractional maximal functions"},"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":"1105.2661","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-13T08:45:14Z","cross_cats_sorted":[],"title_canon_sha256":"f7886ec50700975430c882937e773ed4a813ba1fb1b9ba1305589e0cb6b3f820","abstract_canon_sha256":"aa3e7835730626cb16b34afe63e872d4ccbbb3eb78d253c238131ebec80110e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:41.858230Z","signature_b64":"k+InFQP+Ge89y0Gzd9F0K2JRU7zilwTF5bBtCLjhQNTlUpjzmFUkkXBsEb41jYQ+PbngU5jSWmLuGV/NmPuPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a5d534a577322a3c8e5ab0c2ae16b65cc0325c203fce4d56cb9db75719b8469","last_reissued_at":"2026-05-18T03:37:41.857752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:41.857752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-weight norm inequalities for potential type and maximal operators in a metric space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Anna Kairema","submitted_at":"2011-05-13T08:45:14Z","abstract_excerpt":"We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty annulus property, which appeared in earlier works on the subject. One of the new ingredients in the proof is the use of a finite collection of adjacent dyadic systems recently constructed by the author and T. Hyt\\\"onen. We further extend the previous Euclidean characterization of two-weight norm inequalities for fractional maximal functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2661","kind":"arxiv","version":8},"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":"1105.2661","created_at":"2026-05-18T03:37:41.857816+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.2661v8","created_at":"2026-05-18T03:37:41.857816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2661","created_at":"2026-05-18T03:37:41.857816+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJOVGSSXOMRK","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJOVGSSXOMRKHSHF","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJOVGSSX","created_at":"2026-05-18T12:26:34.985390+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/LJOVGSSXOMRKHSHFVMGCVYLLMX","json":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX.json","graph_json":"https://pith.science/api/pith-number/LJOVGSSXOMRKHSHFVMGCVYLLMX/graph.json","events_json":"https://pith.science/api/pith-number/LJOVGSSXOMRKHSHFVMGCVYLLMX/events.json","paper":"https://pith.science/paper/LJOVGSSX"},"agent_actions":{"view_html":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX","download_json":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX.json","view_paper":"https://pith.science/paper/LJOVGSSX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.2661&json=true","fetch_graph":"https://pith.science/api/pith-number/LJOVGSSXOMRKHSHFVMGCVYLLMX/graph.json","fetch_events":"https://pith.science/api/pith-number/LJOVGSSXOMRKHSHFVMGCVYLLMX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX/action/storage_attestation","attest_author":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX/action/author_attestation","sign_citation":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX/action/citation_signature","submit_replication":"https://pith.science/pith/LJOVGSSXOMRKHSHFVMGCVYLLMX/action/replication_record"}},"created_at":"2026-05-18T03:37:41.857816+00:00","updated_at":"2026-05-18T03:37:41.857816+00:00"}