{"paper":{"title":"A bound for Mean values of Fourier transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michel Weber","submitted_at":"2011-05-16T09:53:21Z","abstract_excerpt":"We show that there exists a sequence $\\{n_k, k\\ge 1\\}$ growing at least geometrically such that for any finite non-negative measure $\\nu$ such that $\\hat \\nu\\ge 0$, any $T>0$, $$ \\int_{-2^{n_k} T}^{2^{n_k} T} \\hat \\nu(x) \\dd x \\ll_\\e T\\,2^{2^{(1+\\e)n_k}} \\int_\\R \\Big|{\\sin {xT} \\over xT} \\Big|^{n_k^2} \\nu(\\dd x). $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3048","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"}