{"paper":{"title":"Remez-Type Inequality for Smooth Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yosef Yomdin","submitted_at":"2013-06-16T08:36:27Z","abstract_excerpt":"The classical Remez inequality bounds the maximum of the absolute value of a polynomial $P(x)$ of degree $d$ on $[-1,1]$ through the maximum of its absolute value on any subset $Z$ of positive measure in $[-1,1]$. Similarly, in several variables the maximum of the absolute value of a polynomial $P(x)$ of degree $d$ on the unit ball $B^n \\subset {\\mathbb R}^n$ can be bounded through the maximum of its absolute value on any subset $Z\\subset Q^n_1$ of positive $n$-measure $m_n(Z)$. In \\cite{Yom} a stronger version of Remez inequality was obtained: the Lebesgue $n$-measure $m_n$ was replaced by a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3641","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"}