{"paper":{"title":"Generalized Hilbert operators on weighted Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2012-10-11T18:32:20Z","abstract_excerpt":"The main purpose of this paper is to study the generalized Hilbert operator\n  {equation*}\n  \\mathcal{H}_g(f)(z)=\\int_0^1f(t)g'(tz)\\,dt\n  {equation*} acting on the weighted Bergman space $A^p_\\om$, where the weight function $\\om$ belongs to the class $\\R$ of regular radial weights and satisfies the Muckenhoupt type condition\n  {equation}\\label{Mpconditionaabstract}\n  \\sup_{0\\le r<1}\\bigg(\\int_{r}^1(\\int_t^1\\om(s)ds)^{-\\frac{p'}{p}}\\,dt\\bigg)^\\frac{p}{p'}\n  \\int_{0}^r(1-t)^{-p}(\\int_t^1\\om(s)ds)\\,dt<\\infty. \\tag{\\dag}\n  {equation} If $q=p$, the condition on $g$ that characterizes the boundedness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3315","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"}