{"paper":{"title":"Quantitative estimates in Beurling--Helson type theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Lebedev","submitted_at":"2011-12-24T00:29:37Z","abstract_excerpt":"We consider the spaces $A_p(\\mathbb T)$ of functions $f$ on the circle $\\mathbb T$ such that the sequence of Fourier coefficients $\\fu{\\f}=\\{\\fu{\\f}(k), ~k \\in \\mathbb Z\\}$ belongs to $l^p, ~1\\leq p<2$. The norm on $A_p(\\mathbb T)$ is defined by $\\|f\\|_{A_p}=\\|\\fu{\\f}\\nolinebreak\\|_{l^p}$. We study the rate of growth of the norms $\\|e^{i\\lambda\\varphi}\\|_{A_p}$ as $|\\lambda|\\rightarrow \\infty, ~\\lambda\\in\\mathbb R,$ for $C^1$ -smooth real functions $\\varphi$ on $\\mathbb T$. The results have natural applications to the problem on changes of variable in the spaces $A_p(\\mathbb T)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5677","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"}