{"paper":{"title":"Norming Sets and Related Remez-type Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Brudnyi, Y. Yomdin","submitted_at":"2013-12-20T17:16:52Z","abstract_excerpt":"The classical Remez inequality bounds the maximum of the absolute value of a real polynomial $P$ of degree $d$ on $[-1,1]$ through the maximum of its absolute value on any subset $Z\\subset [-1,1]$ of positive Lebesgue measure. Extensions to several variables and to certain sets of Lebesgue measure zero, massive in a much weaker sense, are available.\n  Still, given a subset $Z\\subset [-1,1]^n\\subset {\\mathbb R}^n$ it is not easy to determine whether it is ${\\mathcal P}_d({\\mathbb R}^n)$-norming (here ${\\mathcal P}_d({\\mathbb R}^n)$ is the space of real polynomials of degree at most $d$ on ${\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6050","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"}