{"paper":{"title":"Sharp norm estimates for composition operators and Hilbert-type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Ole Fredrik Brevig","submitted_at":"2017-05-03T09:05:29Z","abstract_excerpt":"Let $\\mathscr{H}^2$ denote the Hardy space of Dirichlet series $f(s) = \\sum_{n\\geq1} a_n n^{-s}$ with square summable coefficients and suppose that $\\varphi$ is a symbol generating a composition operator on $\\mathscr{H}^2$ by $\\mathscr{C}_\\varphi(f) = f \\circ \\varphi$. Let $\\zeta$ denote the Riemann zeta function and $\\alpha_0=1.48\\ldots$ the unique positive solution of the equation $\\alpha\\zeta(1+\\alpha)=2$. We obtain sharp upper bounds for the norm of $\\mathscr{C}_\\varphi$ on $\\mathscr{H}^2$ when $0<\\operatorname{Re}\\varphi(+\\infty)-1/2 \\leq \\alpha_0$, by relating such sharp upper bounds to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01316","kind":"arxiv","version":2},"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"}