{"paper":{"title":"Atomic decomposition and Carleson measures for weighted mixed norm spaces","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, Kian Sierra","submitted_at":"2017-09-21T10:00:37Z","abstract_excerpt":"The purpose of this paper is to establish an atomic decomposition for functions in the weighted mixed norm space $A^{p,q}_\\omega$ induced by a radial weight $\\omega$ in the unit disc admitting a two-sided doubling condition. The obtained decomposition is further applied to characterize Carleson measures for $A^{p,q}_\\omega$, and bounded differentiation operators $D^{(n)}(f)=f^{(n)}$ acting from $A^{p,q}_\\omega$ to $L^p_\\mu$, induced by a positive Borel measure $\\mu$, on the full range of parameters $0<p,q,s<\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07239","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"}