{"paper":{"title":"Analytic version of critical $Q$ spaces and their properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Junming Liu, Pengtao Li, Zengjian Lou","submitted_at":"2014-06-05T08:56:05Z","abstract_excerpt":"In this paper, we establish an analytic version of critical spaces $Q_{\\alpha}^{\\beta}(\\mathbb{R}^{n})$ on unit disc $\\mathbb{D}$, denoted by $Q^{\\beta}_{p}(\\mathbb{D})$. Further we prove a relation between $Q^{\\beta}_{p}(\\mathbb{D})$ and Morrey spaces. By the boundedness of two integral operators, we give the multiplier spaces of $Q^{\\beta}_{p}(\\mathbb{D})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1299","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"}