{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:R66HPLQL5VDGCYFN6Z2SCM3RAD","short_pith_number":"pith:R66HPLQL","schema_version":"1.0","canonical_sha256":"8fbc77ae0bed466160adf67521337100f47640a717c759d69e6706571db51e25","source":{"kind":"arxiv","id":"1907.10563","version":1},"attestation_state":"computed","paper":{"title":"Harmonic conjugates on Bergman spaces induced by doubling weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2019-07-24T17:04:59Z","abstract_excerpt":"A radial weight $\\omega$ belongs to the class $\\widehat{\\mathcal{D}}$ if there exists $C=C(\\omega)\\ge 1$ such that $\\int_r^1 \\omega(s)\\,ds\\le C\\int_{\\frac{1+r}{2}}^1\\omega(s)\\,ds$ for all $0\\le r<1$. Write $\\omega\\in\\check{\\mathcal{D}}$ if there exist constants $K=K(\\omega)>1$ and $C=C(\\omega)>1$ such that $\\widehat{\\omega}(r)\\ge C\\widehat{\\omega}\\left(1-\\frac{1-r}{K}\\right)$ for all $0\\le r<1$. In a recent paper, we have recently prove that these classes of radial weights arise naturally in the operator theory of Bergman spaces induced by radial weights.\n  Classical results by Hardy and Littl"},"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":"1907.10563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-07-24T17:04:59Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"31620865a55207276f77cae6faa4789153df9b49ae198eca41b860bb44888eb5","abstract_canon_sha256":"7ad4743356433447e621810008f3a9add530854784a91da6909d76f8cca891e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:37.552589Z","signature_b64":"NA+g9io0dsuryeCgvt5hbUD7VgZI3PMJizU29yvTHKLmuRw3XfEpF/WKpboeRrfj/KYyRUtSovirF1flerNGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fbc77ae0bed466160adf67521337100f47640a717c759d69e6706571db51e25","last_reissued_at":"2026-05-17T23:39:37.551887Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:37.551887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic conjugates on Bergman spaces induced by doubling weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2019-07-24T17:04:59Z","abstract_excerpt":"A radial weight $\\omega$ belongs to the class $\\widehat{\\mathcal{D}}$ if there exists $C=C(\\omega)\\ge 1$ such that $\\int_r^1 \\omega(s)\\,ds\\le C\\int_{\\frac{1+r}{2}}^1\\omega(s)\\,ds$ for all $0\\le r<1$. Write $\\omega\\in\\check{\\mathcal{D}}$ if there exist constants $K=K(\\omega)>1$ and $C=C(\\omega)>1$ such that $\\widehat{\\omega}(r)\\ge C\\widehat{\\omega}\\left(1-\\frac{1-r}{K}\\right)$ for all $0\\le r<1$. In a recent paper, we have recently prove that these classes of radial weights arise naturally in the operator theory of Bergman spaces induced by radial weights.\n  Classical results by Hardy and Littl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10563","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":"1907.10563","created_at":"2026-05-17T23:39:37.551973+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.10563v1","created_at":"2026-05-17T23:39:37.551973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10563","created_at":"2026-05-17T23:39:37.551973+00:00"},{"alias_kind":"pith_short_12","alias_value":"R66HPLQL5VDG","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"R66HPLQL5VDGCYFN","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"R66HPLQL","created_at":"2026-05-18T12:33:27.125529+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/R66HPLQL5VDGCYFN6Z2SCM3RAD","json":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD.json","graph_json":"https://pith.science/api/pith-number/R66HPLQL5VDGCYFN6Z2SCM3RAD/graph.json","events_json":"https://pith.science/api/pith-number/R66HPLQL5VDGCYFN6Z2SCM3RAD/events.json","paper":"https://pith.science/paper/R66HPLQL"},"agent_actions":{"view_html":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD","download_json":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD.json","view_paper":"https://pith.science/paper/R66HPLQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.10563&json=true","fetch_graph":"https://pith.science/api/pith-number/R66HPLQL5VDGCYFN6Z2SCM3RAD/graph.json","fetch_events":"https://pith.science/api/pith-number/R66HPLQL5VDGCYFN6Z2SCM3RAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD/action/storage_attestation","attest_author":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD/action/author_attestation","sign_citation":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD/action/citation_signature","submit_replication":"https://pith.science/pith/R66HPLQL5VDGCYFN6Z2SCM3RAD/action/replication_record"}},"created_at":"2026-05-17T23:39:37.551973+00:00","updated_at":"2026-05-17T23:39:37.551973+00:00"}