{"paper":{"title":"Lp mean estimates for an operator preserving inequalities between polynomials","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"N. A. Rather, Suhail Gulzar","submitted_at":"2013-06-04T09:59:35Z","abstract_excerpt":"If $P(z)$ be a polynomial of degree at most $n$ which does not vanish in $|z| < 1$, it was recently formulated by Shah and Liman \\cite[\\textit{Integral estimates for the family of $B$-operators, Operators and Matrices,} \\textbf{5}(2011), 79 - 87]{wl} that for every $R\\geq 1$, $p\\geq 1$,\n  \\[\\left\\|B[P\\circ\\sigma](z)\\right\\|_p \\leq\\frac{R^{n}|\\Lambda_n|+|\\lambda_{0}|}{\\left\\|1+z\\right\\|_p}\\left\\|P(z)\\right\\|_p,\\] where $B$ is a $ \\mathcal{B}_{n}$-operator with parameters $\\lambda_{0}, \\lambda_{1}, \\lambda_{2}$ in the sense of Rahman \\cite{qir}, $\\sigma(z)=Rz$ and $\\Lambda_n=\\lambda_{0}+\\lambda_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0714","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"}