{"paper":{"title":"Arestov's theorems on Bernstein's inequality","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tam\\'as Erd\\'elyi","submitted_at":"2019-04-26T15:12:56Z","abstract_excerpt":"We give a simple, elementary, and at least partially new proof of Arestov's famous extension of Bernstein's inequality in $L_p$ to all $p \\geq 0$. Our crucial observation is that Boyd's approach to prove Mahler's inequality for algebraic polynomials $P_n \\in {\\mathcal P}_n^c$ can be extended to all trigonometric polynomials $T_n \\in {\\mathcal T}_n^c$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11887","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"}