{"paper":{"title":"Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Koebe function achieves the sharp multiplier norms for its higher-order Schwarzian derivatives between weighted Bergman spaces.","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jianjun Jin","submitted_at":"2026-04-22T08:21:23Z","abstract_excerpt":"In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function. This extends a related result by Shimorin. The proof of our new theorem relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work. We finally point out that the Koebe function is still the extremal function for c"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proof relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Sharp multiplier estimates are established for the higher-order Schwarzian derivatives of the Koebe function in weighted Bergman spaces.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Koebe function achieves the sharp multiplier norms for its higher-order Schwarzian derivatives between weighted Bergman spaces.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0df3ec7e23e369c9f7afafdd5d1537d82449c1caa0dd5f1914d3500bbd00204c"},"source":{"id":"2604.20326","kind":"arxiv","version":5},"verdict":{"id":"a3fd55f3-0142-4897-89da-84fc105b5e51","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T23:00:46.681342Z","strongest_claim":"We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function.","one_line_summary":"Sharp multiplier estimates are established for the higher-order Schwarzian derivatives of the Koebe function in weighted Bergman spaces.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proof relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work.","pith_extraction_headline":"The Koebe function achieves the sharp multiplier norms for its higher-order Schwarzian derivatives between weighted Bergman spaces."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.20326/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}