{"paper":{"title":"The Bloch space and the dual space of a Luecking-type subspace of $A^1$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Fangqin Ye, Guanlong Bao","submitted_at":"2017-05-23T18:25:09Z","abstract_excerpt":"Let $X$ be the dual space of a Luecking-type subspace of the Bergman space $A^1$. It is known that the Bloch space $\\mathcal{B}$ is a subset of $X$. In 1990, Ghatage and Sun asked whether $\\mathcal{B}$ is dense in $X$. They also asked whether the little version of $X$ is a subset of $\\mathcal{B}$. In this note, based on results and methods of Girela, Pel\\'aez, P\\'erez-Gonz\\'alez and R\\\"atty\\\"a in 2008, we answer the two questions in the negative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08466","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"}