{"paper":{"title":"The Fourier transform is an extremizer of a class of bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Miquel Saucedo, Sergey Tikhonov","submitted_at":"2025-01-29T09:22:57Z","abstract_excerpt":"We show that, for a natural class of rearrangement admissible spaces $X$ and $Y$, the Fourier operator is bounded between $X$ and $Y$ if and only if any operator of joint strong type $(1,\\infty; 2,2)$ is also bounded between $X$ and $Y$.\n  By using this result, we fully characterize the weighted Fourier inequalities of the form $$\\qquad\\qquad \\lVert\\widehat{f}u \\rVert_q \\leq C \\lVert fv\\rVert_p,\\quad 1\\leq p\\leq \\infty,\\,0<q\\leq \\infty,$$ for radially monotone weights $(u,v)$.\n  This answers a long-standing problem posed by Benedetto-Heinig, Jurkat-Sampson, and Muckenhoupt. In the case of $p\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.17505","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.17505/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}