{"paper":{"title":"Markov $L_2$-inequality with the Laguerre 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":"2017-05-10T15:41:51Z","abstract_excerpt":"Let $w_\\alpha(t) := t^{\\alpha}\\,e^{-t}$, where $\\alpha > -1$, be the Laguerre weight function, and let $\\|\\cdot\\|_{w_\\alpha}$ be the associated $L_2$-norm, $$ \\|f\\|_{w_\\alpha} = \\left\\{\\int_{0}^{\\infty} |f(x)|^2 w_\\alpha(x)\\,dx\\right\\}^{1/2}\\,. $$ By $\\mathcal{P}_n$ we denote the set of algebraic polynomials of degree $\\le n$.\n  We study the best constant $c_n(\\alpha)$ in the Markov inequality in this norm $$ \\|p_n'\\|_{w_\\alpha} \\le c_n(\\alpha) \\|p_n\\|_{w_\\alpha}\\,,\\qquad p_n \\in \\mathcal{P}_n\\,, $$ namely the constant $$ c_n(\\alpha) := \\sup_{p_n \\in \\mathcal{P}_n} \\frac{\\|p_n'\\|_{w_\\alpha}}{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03824","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"}