{"paper":{"title":"Markov $L_2$ inequality with the Gegenbauer weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dragomir Aleksov, Geno Nikolov","submitted_at":"2017-02-20T13:42:38Z","abstract_excerpt":"For the Gegenbauer weight function $w_{\\lambda}(t)=(1-t^2)^{\\lambda-1/2}$, $\\lambda>-1/2$, we denote by $\\Vert\\cdot\\Vert_{w_{\\lambda}}$ the associated $L_2$-norm, $$ \\Vert f\\Vert_{w_{\\lambda}}:=\\Big(\\int_{-1}^{1}w_{\\lambda}(t)f^2(t)\\,dt\\Big)^{1/2}. $$ We study the Markov inequality $$ \\Vert p^{\\prime}\\Vert_{w_{\\lambda}}\\leq c_{n}(\\lambda)\\,\\Vert p\\Vert_{w_{\\lambda}},\\qquad p\\in \\mathcal{P}_n, $$ where $\\mathcal{P}_n$ is the class of algebraic polynomials of degree not exceeding $n$. Upper and lower bounds for the best Markov constant $c_{n}(\\lambda)$ are obtained, which are valid for all $n\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05963","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"}