{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5TZFU5M6BEYBN63YUGEDS73ATR","short_pith_number":"pith:5TZFU5M6","schema_version":"1.0","canonical_sha256":"ecf25a759e093016fb78a188397f609c73787c18f899b262974a49b224bfc580","source":{"kind":"arxiv","id":"1305.1127","version":1},"attestation_state":"computed","paper":{"title":"Harmonic Bergman spaces, the Poisson equation and the dual of Hardy-type spaces on certain noncompact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. Mauceri, M. Vallarino, S. Meda","submitted_at":"2013-05-06T09:29:47Z","abstract_excerpt":"In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We realize the dual space Y^h(M) of the Hardy-type space X^h(M), introduced in a previous paper of the authors, as the class of all locally square integrable functions satisfying suitable BMO-like conditions, where the role of the constants is played by the space of global k-quasi-harmonic functions. Furthermore we prove that Y^h(M) is also the dual of the space X^k_fin(M) of finite linear combination of X^k-atoms. As a consequence, if Z is a Banach space and T is a Z-valued "},"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":"1305.1127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-06T09:29:47Z","cross_cats_sorted":[],"title_canon_sha256":"2ab889e5eda86d42f6b955e02b3ed1d6a15aa74f9f50b655d36761e513127808","abstract_canon_sha256":"f21bbeb9cc0c8b3c402e834653f9fea78b3868cf0631b54a88b8bd601ebdbd5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:24.080774Z","signature_b64":"KpeaAtvuQBB//O9JA4EQtLD4ojfhEBJ7XvvK5G/UB0NeOUhi1cP+lx2gGhqKKmqrne780b/E5uJ08MqyaKMMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecf25a759e093016fb78a188397f609c73787c18f899b262974a49b224bfc580","last_reissued_at":"2026-05-18T03:26:24.080197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:24.080197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic Bergman spaces, the Poisson equation and the dual of Hardy-type spaces on certain noncompact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. Mauceri, M. Vallarino, S. Meda","submitted_at":"2013-05-06T09:29:47Z","abstract_excerpt":"In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We realize the dual space Y^h(M) of the Hardy-type space X^h(M), introduced in a previous paper of the authors, as the class of all locally square integrable functions satisfying suitable BMO-like conditions, where the role of the constants is played by the space of global k-quasi-harmonic functions. Furthermore we prove that Y^h(M) is also the dual of the space X^k_fin(M) of finite linear combination of X^k-atoms. As a consequence, if Z is a Banach space and T is a Z-valued "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1127","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":"1305.1127","created_at":"2026-05-18T03:26:24.080283+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.1127v1","created_at":"2026-05-18T03:26:24.080283+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1127","created_at":"2026-05-18T03:26:24.080283+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TZFU5M6BEYB","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TZFU5M6BEYBN63Y","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TZFU5M6","created_at":"2026-05-18T12:27:34.582898+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/5TZFU5M6BEYBN63YUGEDS73ATR","json":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR.json","graph_json":"https://pith.science/api/pith-number/5TZFU5M6BEYBN63YUGEDS73ATR/graph.json","events_json":"https://pith.science/api/pith-number/5TZFU5M6BEYBN63YUGEDS73ATR/events.json","paper":"https://pith.science/paper/5TZFU5M6"},"agent_actions":{"view_html":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR","download_json":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR.json","view_paper":"https://pith.science/paper/5TZFU5M6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.1127&json=true","fetch_graph":"https://pith.science/api/pith-number/5TZFU5M6BEYBN63YUGEDS73ATR/graph.json","fetch_events":"https://pith.science/api/pith-number/5TZFU5M6BEYBN63YUGEDS73ATR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR/action/storage_attestation","attest_author":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR/action/author_attestation","sign_citation":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR/action/citation_signature","submit_replication":"https://pith.science/pith/5TZFU5M6BEYBN63YUGEDS73ATR/action/replication_record"}},"created_at":"2026-05-18T03:26:24.080283+00:00","updated_at":"2026-05-18T03:26:24.080283+00:00"}