{"paper":{"title":"Bernstein inequalities with nondoubling weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andriy Bondarenko, Sergey Tikhonov","submitted_at":"2013-08-27T10:32:20Z","abstract_excerpt":"We answer Totik's question on weighted Bernstein's inequalities showing that $$ \\|T_n'\\|_{L_p(\\omega)} \\le C(p,\\omega)\\, {n}\\,\\|T_n\\|_{L_p(\\omega)},\\qquad 0<p\\le \\infty, $$ holds for all trigonometric polynomials $T_n$ and certain nondoubling weights $\\omega$. Moreover, we find necessary conditions on $\\omega$ for Bernstein's inequality to hold. We also prove weighted Bernstein-Markov, Remez, and Nikolskii inequalities for trigonometric and algebraic polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5818","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"}