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It is known that the following inequality $$ |f(0)|+\\sup_{w\\in \\D} \\left(\\int_\\D \\left|\\frac{f(z)-f(w)}{1-\\overline{w}z}\\right|^2 (1-|\\sigma_w(z)|^2)^p dA(z)\\right)^{1/2} \\lesssim \\|f\\|_{\\mathcal{Q}_p} $$ played a key role to characterize mult"},"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":"1810.05901","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-13T17:40:05Z","cross_cats_sorted":[],"title_canon_sha256":"57738cf7402a55423c94e5c020b3f419113ea9490010e27416e2121f8f8834ec","abstract_canon_sha256":"d5e3f2600e3fb303d47abdb4561ccd28b8c724c58a7b5c78f28831bf65916adc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:58.192411Z","signature_b64":"AET62sJBwQI5SWiAII/lM9Uc0tPVuKnynCuMRvBnqnetcoqskXACkIWt8cOAqjWKsJ/JAstb6n4TyMMkHaO9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a34dfc2c55c2f81db692d7a6857dbad59acc594371e7e9653586dbe1b32e860","last_reissued_at":"2026-05-17T23:56:58.191665Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:58.191665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An inequality associated with $\\mathcal{Q}_p$ functions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Fangqin Ye, Guanlong Bao","submitted_at":"2018-10-13T17:40:05Z","abstract_excerpt":"The M\\\"obius invariant space $\\mathcal{Q}_p$, $0<p<\\infty$, consists of functions $f$ which are analytic in the open unit disk $\\mathbb{D}$ with $$ \\|f\\|_{\\mathcal{Q}_p}=|f(0)|+\\sup_{w\\in \\D} \\left(\\int_\\D |f'(z)|^2(1-|\\sigma_w(z)|^2)^p dA(z)\\right)^{1/2}<\\infty, $$ where $\\sigma_w(z)=(w-z)/(1-\\overline{w}z)$ and $dA$ is the area measure on $\\mathbb{D}$. It is known that the following inequality $$ |f(0)|+\\sup_{w\\in \\D} \\left(\\int_\\D \\left|\\frac{f(z)-f(w)}{1-\\overline{w}z}\\right|^2 (1-|\\sigma_w(z)|^2)^p dA(z)\\right)^{1/2} \\lesssim \\|f\\|_{\\mathcal{Q}_p} $$ played a key role to characterize mult"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05901","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":""},"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":"1810.05901","created_at":"2026-05-17T23:56:58.191781+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.05901v2","created_at":"2026-05-17T23:56:58.191781+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05901","created_at":"2026-05-17T23:56:58.191781+00:00"},{"alias_kind":"pith_short_12","alias_value":"NI2N7QWFLQXY","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NI2N7QWFLQXYDW3J","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NI2N7QWF","created_at":"2026-05-18T12:32:40.477152+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/NI2N7QWFLQXYDW3JFV5GQV63VV","json":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV.json","graph_json":"https://pith.science/api/pith-number/NI2N7QWFLQXYDW3JFV5GQV63VV/graph.json","events_json":"https://pith.science/api/pith-number/NI2N7QWFLQXYDW3JFV5GQV63VV/events.json","paper":"https://pith.science/paper/NI2N7QWF"},"agent_actions":{"view_html":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV","download_json":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV.json","view_paper":"https://pith.science/paper/NI2N7QWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.05901&json=true","fetch_graph":"https://pith.science/api/pith-number/NI2N7QWFLQXYDW3JFV5GQV63VV/graph.json","fetch_events":"https://pith.science/api/pith-number/NI2N7QWFLQXYDW3JFV5GQV63VV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV/action/storage_attestation","attest_author":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV/action/author_attestation","sign_citation":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV/action/citation_signature","submit_replication":"https://pith.science/pith/NI2N7QWFLQXYDW3JFV5GQV63VV/action/replication_record"}},"created_at":"2026-05-17T23:56:58.191781+00:00","updated_at":"2026-05-17T23:56:58.191781+00:00"}