{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GUNRO3J6CVZKKKHODCKEFNSNPT","short_pith_number":"pith:GUNRO3J6","schema_version":"1.0","canonical_sha256":"351b176d3e1572a528ee189442b64d7cdcdebe93942152c2cad947a0a3be6c3e","source":{"kind":"arxiv","id":"1906.11934","version":1},"attestation_state":"computed","paper":{"title":"Bounded point derivations and functions of bounded mean oscillation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Stephen Deterding","submitted_at":"2019-06-27T20:03:54Z","abstract_excerpt":"Let $X$ be a subset of the complex plane and let $A_0(X)$ denote the space of VMO functions that are analytic on $X$. $A_0(X)$ is said to admit a bounded point derivation of order $t$ at a point $x_0 \\in \\partial X$ if there exists a constant $C$ such that $|f^{(t)}(x_0)|\\leq C ||f||_{BMO}$ for all functions in $VMO(X)$ that are analytic on $X \\cup \\{x_0\\}$. In this paper, we give necessary and sufficient conditions in terms of lower $1$-dimensional Hausdorff content for $A_0(X)$ to admit a bounded point derivation at $x_0$. These conditions are similar to conditions for the existence of bound"},"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":"1906.11934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-06-27T20:03:54Z","cross_cats_sorted":[],"title_canon_sha256":"1b246a34768b99b7ff5c0861d6d2136d7052f51d4cc1eb1684f8a99f93716b87","abstract_canon_sha256":"94e64231682ea0af158543d6fccda07d0a8f1cc4ba19b7e61ce8d0b719a59d51"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:01.547799Z","signature_b64":"L+klMjV1nMNt0WOpX8BD+LKitZqMbvBOih5Q6KiqUUu8fcIHbzwHcna4l2uaLwa4akpuaLyYr2+NEqMhqYLIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"351b176d3e1572a528ee189442b64d7cdcdebe93942152c2cad947a0a3be6c3e","last_reissued_at":"2026-05-17T23:42:01.547145Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:01.547145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded point derivations and functions of bounded mean oscillation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Stephen Deterding","submitted_at":"2019-06-27T20:03:54Z","abstract_excerpt":"Let $X$ be a subset of the complex plane and let $A_0(X)$ denote the space of VMO functions that are analytic on $X$. $A_0(X)$ is said to admit a bounded point derivation of order $t$ at a point $x_0 \\in \\partial X$ if there exists a constant $C$ such that $|f^{(t)}(x_0)|\\leq C ||f||_{BMO}$ for all functions in $VMO(X)$ that are analytic on $X \\cup \\{x_0\\}$. In this paper, we give necessary and sufficient conditions in terms of lower $1$-dimensional Hausdorff content for $A_0(X)$ to admit a bounded point derivation at $x_0$. These conditions are similar to conditions for the existence of bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11934","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":"1906.11934","created_at":"2026-05-17T23:42:01.547255+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.11934v1","created_at":"2026-05-17T23:42:01.547255+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11934","created_at":"2026-05-17T23:42:01.547255+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUNRO3J6CVZK","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUNRO3J6CVZKKKHO","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUNRO3J6","created_at":"2026-05-18T12:33:18.533446+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/GUNRO3J6CVZKKKHODCKEFNSNPT","json":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT.json","graph_json":"https://pith.science/api/pith-number/GUNRO3J6CVZKKKHODCKEFNSNPT/graph.json","events_json":"https://pith.science/api/pith-number/GUNRO3J6CVZKKKHODCKEFNSNPT/events.json","paper":"https://pith.science/paper/GUNRO3J6"},"agent_actions":{"view_html":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT","download_json":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT.json","view_paper":"https://pith.science/paper/GUNRO3J6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.11934&json=true","fetch_graph":"https://pith.science/api/pith-number/GUNRO3J6CVZKKKHODCKEFNSNPT/graph.json","fetch_events":"https://pith.science/api/pith-number/GUNRO3J6CVZKKKHODCKEFNSNPT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT/action/storage_attestation","attest_author":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT/action/author_attestation","sign_citation":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT/action/citation_signature","submit_replication":"https://pith.science/pith/GUNRO3J6CVZKKKHODCKEFNSNPT/action/replication_record"}},"created_at":"2026-05-17T23:42:01.547255+00:00","updated_at":"2026-05-17T23:42:01.547255+00:00"}