{"paper":{"title":"Embedding theorems for Bergman spaces via harmonic analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2014-11-06T16:06:44Z","abstract_excerpt":"Let $A^p_\\omega$ denote the Bergman space in the unit disc induced by a radial weight~$\\omega$ with the doubling property $\\int_{r}^1\\omega(s)\\,ds\\le C\\int_{\\frac{1+r}{2}}^1\\omega(s)\\,ds$. The positive Borel measures such that the differentiation operator of order $n\\in\\mathbb{N}\\cup\\{0\\}$ is bounded from $A^p_\\omega$ into $L^q(\\mu)$ are characterized in terms of geometric conditions when $0<p,q<\\infty$. En route to the proof a theory of tent spaces for weighted Bergman spaces is built."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1648","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"}