{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TH3IGSVOWPULCQZVJX6HR5KHME","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"699c8a60e4fd63496bb79a66315e8fb65a43ff75efed0b0c7ec581b894604ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-16T18:57:59Z","title_canon_sha256":"8954e76128a1ac62104088525da416b56449998e1fc403b1ec223f0408387e40"},"schema_version":"1.0","source":{"id":"1504.04338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04338","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04338v1","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04338","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"TH3IGSVOWPUL","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TH3IGSVOWPULCQZV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TH3IGSVO","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:f64c55ca3e70ad6165ff7295295ada0101a21147f49621645edb6e74a6f9f2dc","target":"graph","created_at":"2026-05-18T02:18:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For $1<p<\\infty$ and $0<s<1$, let $\\mathcal{Q}^p_ s (\\mathbb{T})$ be the space of those functions $f$ which belong to\n  $ L^p(\\mathbb{T})$ and satisfy \\[ \\sup_{I\\subset \\mathbb{T}}\\frac{1}{|I|^s}\\int_I\\int_I\\frac{|f(\\zeta)-f(\\eta)|^p}{|\\zeta-\\eta|^{2-s}}|d\\zeta||d\\eta|<\\infty, \\] where $|I|$ is the length of an arc $I$ of the unit circle $\\mathbb{T}$ . In this paper, we give a complete description of multipliers between $\\mathcal{Q}^p_ s (\\mathbb{T})$ spaces. The spectra of multiplication operators on $\\mathcal{Q}^p_ s (\\mathbb{T})$ are also obtained.","authors_text":"Guanlong Bao, Jordi Pau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-16T18:57:59Z","title":"Boundary multipliers of a family of M\\\"obius invariant function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04338","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:69534d22347da11fa866d7e88c32c2893dcdab1214bdc3bbaad95476e72b143d","target":"record","created_at":"2026-05-18T02:18:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"699c8a60e4fd63496bb79a66315e8fb65a43ff75efed0b0c7ec581b894604ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-16T18:57:59Z","title_canon_sha256":"8954e76128a1ac62104088525da416b56449998e1fc403b1ec223f0408387e40"},"schema_version":"1.0","source":{"id":"1504.04338","kind":"arxiv","version":1}},"canonical_sha256":"99f6834aaeb3e8b143354dfc78f5476120727b2da11e30e00828f095c6f8a5cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99f6834aaeb3e8b143354dfc78f5476120727b2da11e30e00828f095c6f8a5cb","first_computed_at":"2026-05-18T02:18:33.417474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:33.417474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MOHQd3FhMxkjSUn43FTVgxRP5YMaTbPL2qtssiRc5GgaA2H8ZKpGQElpr/NGmVnnZx2M8v6jYu64V14cpjT1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:33.417922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69534d22347da11fa866d7e88c32c2893dcdab1214bdc3bbaad95476e72b143d","sha256:f64c55ca3e70ad6165ff7295295ada0101a21147f49621645edb6e74a6f9f2dc"],"state_sha256":"022617746afc7cab0dcc89716d4e176a421b6900a7d2a87fa367f6a24f7f80f5"}