{"paper":{"title":"On the Markov inequality in the $L_2$-norm with Gegenbauer weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Shadrin, Dragomir Aleksov, Geno Nikolov","submitted_at":"2015-10-12T13:00:27Z","abstract_excerpt":"Let $w_{\\lambda}(t)=(1-t^2)^{\\lambda-1/2}$, $\\lambda>-1/2$, be the Gegenbauer weight function, and $\\Vert\\cdot\\Vert$ denote the associated $L_2$-norm, i.e., $$ \\Vert f\\Vert:=\\Big(\\int_{-1}^{1}w_{\\lambda}(t)\\vert f(t)\\vert^2\\,dt\\Big)^{1/2}. $$ Denote by $\\mathcal{P}_n$ the set of algebraic polynomials of degree not exceeding $n$. We study the best (i.e., the smallest) constant $c_{n,\\lambda}$ in the Markov inequality $$ \\Vert p^{\\prime}\\Vert\\leq c_{n,\\lambda}\\,\\Vert p\\Vert,\\qquad p\\in \\mathcal{P}_n, $$ and prove that $$ c_{n,\\lambda}< \\frac{(n+1)(n+2\\lambda+1)}{2\\sqrt{2\\lambda+1}},\\qquad \\lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03265","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"}