{"paper":{"title":"A generalized Hilbert matrix acting on Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Christos Chatzifountas, Daniel Girela, Jose Angel Pelaez","submitted_at":"2013-09-24T12:08:11Z","abstract_excerpt":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$, the Hankel matrix $\\mathcal H_\\mu =(\\mu_{n,k})_{n,k\\ge 0}$ with entries $\\mu_{n,k}=\\int_{[0,1)}t^{n+k}\\,d\\mu(t)$ induces formally the operator $$\\mathcal{H}_\\mu (f)(z)=\\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty}\\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\mathbb{D} $. In this paper we describe those measures $\\mu$ for which $\\mathcal{H}_\\mu $ is a bounded (compact) operator from $H^p$ into $H^q$, $0<p,q<\\infty $. We also characterize the measures $\\mu $ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6125","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"}