{"paper":{"title":"Multipliers of Dirichlet subspaces of the Bloch space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Christos Chatzifountas, Daniel Girela, Jos\\'e \\'Angel Pel\\'aez","submitted_at":"2012-11-24T20:01:00Z","abstract_excerpt":"For $0<p<\\infty $ we let $\\mathcal D^p_{p-1}$ denote the space of those functions $f$ which are analytic in the unit disc $\\mathbb D $ and satisfy $\\int_\\mathbb D (1-| z|)\\sp {p-1}| f'(z)| \\sp p\\,dA(z)<\\infty $.  \nIt is known that, whenever $p\\neq q$, the only multiplier from $\\mathcal D^p_{p-1} $ to $\\mathcal D^q_{q-1} $ is the trivial one. However, if $X$ is a subspace of the Bloch space and $0<p\\le q<\\infty$, then $X \\cap \\mathcal D^p_{p-1}\\subset X\\cap \\mathcal D^q_{q-1} $, a fact which implies that the space of multipliers $\\M(\\mathcal D^p_{p-1}\\cap X, \\mathcal D^q_{q-1} \\cap X)$ is non-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5703","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"}