{"paper":{"title":"An Extension of the Chen-Beurling-Helson-Lowdenslager Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Don Hadwin, Haihui Fan, Wenjing Liu","submitted_at":"2016-11-01T03:22:52Z","abstract_excerpt":"Yanni Chen extended the classical Beurling-Helson-Lowdenslager Theorem for Hardy spaces on the unit circle $\\mathbb{T}$ defined in terms of continuous gauge norms on $L^{\\infty}$ that dominate $\\Vert\\cdot\\Vert_{1}$. We extend Chen's result to a much larger class of continuous gauge norms. A key ingredient is our result that if $\\alpha$ is a continuous normalized gauge norm on $L^{\\infty}$, then there is a probability measure $\\lambda$, mutually absolutely continuous with respect to Lebesgue measure on $\\mathbb{T}$, such that $\\alpha\\geq c\\Vert\\cdot\\Vert_{1,\\lambda}$ for some $0<c\\leq1.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00357","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"}