{"paper":{"title":"Asymptotics of sharp constants of Markov-Bernstein inequalities in integral norm with Jacobi weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Draux, A.I. Aptekarev, D.N. Tulyakov, V.A. Kalyagin","submitted_at":"2014-05-01T14:24:58Z","abstract_excerpt":"The classical A. Markov inequality establishes a relation between the maximum modulus or the $L^{\\infty}\\left([-1,1]\\right)$ norm of a polynomial $Q_{n}$ and of its derivative: $\\|Q'_{n}\\|\\leqslant M_{n} n^{2}\\|Q_{n}\\|$, where the constant $M_{n}=1$ is sharp. The limiting behavior of the sharp constants $M_{n}$ for this inequality, considered in the space $L^{2}\\left([-1,1], w^{(\\alpha,\\beta)}\\right)$ with respect to the classical Jacobi weight $w^{(\\alpha,\\beta)}(x):=(1-x)^{\\alpha}(x+1)^{\\beta}$, is studied. We prove that, under the condition $|\\alpha - \\beta| < 4 $, the limit is $\\lim_{n \\to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0167","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"}