{"paper":{"title":"On the Markov inequality in the $L_2$-norm with the Gegenbauer weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Shadrin, Geno Nikolov","submitted_at":"2017-01-26T13:15:18Z","abstract_excerpt":"Let $w_{\\lambda}(t) := (1-t^2)^{\\lambda-1/2}$, where $\\lambda > -\\frac{1}{2}$, be the Gegenbauer weight function, let $\\|\\cdot\\|_{w_{\\lambda}}$ be the associated $L_2$-norm, $$\n  \\|f\\|_{w_{\\lambda}} = \\left\\{\\int_{-1}^1 |f(x)|^2 w_{\\lambda}(x)\\,dx\\right\\}^{1/2}\\,, $$ and denote by $\\mathcal{P}_n$ the space of algebraic polynomials of degree $\\le n$.\n  We study the best constant $c_n(\\lambda)$ in the Markov inequality in this norm $$\n  \\|p_n'\\|_{w_{\\lambda}} \\le c_n(\\lambda) \\|p_n\\|_{w_{\\lambda}}\\,,\\qquad p_n \\in \\mathcal{P}_n\\,, $$ namely the constant $$ c_n(\\lambda) := \\sup_{p_n \\in \\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07682","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"}