{"paper":{"title":"Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jizhen Zhou, Songxiao Li","submitted_at":"2018-05-30T13:53:51Z","abstract_excerpt":"Let $\\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\\mathcal{H}_\\mu=(\\mu_{n+k})_{n,k\\geq 0}$ with entries $\\mu_{n,k}=\\mu_{n+k}$ induces the operator $$ \\mathcal{H}_\\mu(f)(z)=\\sum^\\infty_{n=0}\\left(\\sum^\\infty_{k=0}\\mu_{n,k}a_k\\right)z^n $$ on the space of all analytic functions $f(z)=\\sum^\\infty_{n=0}a_nz^n$ in the unit disk $\\mathbb{D}$. In this paper, we characterize the boundedness and compactness of $\\mathcal{H}_\\mu$ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $\\mathcal{H}_\\mu$ from $\\alpha$ Bloch type space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11967","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"}