{"paper":{"title":"On absolute values of QK functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guanlong Bao, Hasi Wulan, Ruishen Qian, Zengjian Lou","submitted_at":"2016-04-09T09:14:13Z","abstract_excerpt":"In this paper, the effect of absolute values on the behavior of functions $f$ in the spaces $\\mathcal{Q}_K$ is investigated. It is clear that $f\\in \\mathcal{Q}_K(\\partial {\\mathbb{D}}) \\Rightarrow |f|\\in \\mathcal{Q}_K(\\partial {\\mathbb{D}})$, but the converse is not always true. For $f$ in the Hardy space $H^2$, we give a condition involving the modulus of the function only, such that this condition together with $|f|\\in \\mathcal{Q}_K(\\partial {\\mathbb{D}})$ is equivalent to $f\\in \\mathcal{Q}_K$. As an application, a new criterion for inner-outer factorisation of $\\mathcal{Q}_K$ spaces is give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02542","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"}