{"paper":{"title":"Norm estimates of weighted composition operators pertaining to the Hilbert Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikael Lindstr\\\"om, Niklas Wikman, Santeri Miihkinen","submitted_at":"2018-05-20T17:43:32Z","abstract_excerpt":"Very recently, Bo\\v{z}in and Karapetrovi\\'c solved a conjecture by proving that the norm of the Hilbert matrix operator $\\mathcal{H}$ on the Bergman space $A^p$ is equal to $\\frac{\\pi}{\\sin(\\frac{2\\pi}{p})}$ for $2 < p < 4.$ In this article we present a partly new and simplified proof of this result. Moreover, we calculate the exact value of the norm of $\\mathcal{H}$ defined on the Korenblum spaces $H^\\infty_\\alpha$ for $0 < \\alpha \\le 2/3$ and an upper bound for the norm on the scale $2/3 < \\alpha < 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07804","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"}