{"paper":{"title":"Convexity, Moduli of Smoothness and a Jackson-Type Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andriy Prymak, Zeev Ditzian","submitted_at":"2014-03-14T16:27:07Z","abstract_excerpt":"For a Banach space $B$ of functions which satisfies for some $m>0$ $$ \\max(\\|F+G\\|_B,\\|F-G\\|_B) \\ge (\\|F\\|^s_B + m\\|G\\|^s_B)^{1/s}, \\forall F,G\\in B \\ (*) $$ a significant improvement for lower estimates of the moduli of smoothness $\\omega^r(f,t)_B$ is achieved. As a result of these estimates, sharp Jackson inequalities which are superior to the classical Jackson type inequality are derived. Our investigation covers Banach spaces of functions on $R^d$ or $T^d$ for which translations are isometries or on $S^{d-1}$ for which rotations are isometries. Results for $C_0$ semigroups of contractions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3632","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"}