{"paper":{"title":"Generalized Hilbert Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Aristomenis Siskakis, Daniel Girela, Jos\\'e \\'Angel Pel\\'aez, Petros Galanopoulos","submitted_at":"2012-09-04T10:35:52Z","abstract_excerpt":"If $g$ is an analytic function in the unit disc $\\D $ we consider the generalized Hilbert operator $\\hg$ defined by {equation*}\\label{H-g} \\mathcal{H}_g(f)(z)=\\int_0^1f(t)g'(tz)\\,dt. {equation*} We study these operators acting on classical spaces of analytic functions in $\\D $. More precisely, we address the question of characterizing the functions $g$ for which the operator $\\hg $ is bounded (compact) on the Hardy spaces $H^p$, on the weighted Bergman spaces $A^p_\\alpha $ or on the spaces of Dirichlet type $\\mathcal D^p_\\alpha $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0594","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"}