{"paper":{"title":"Mapping properties of Fourier transforms, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dorothee D. Haroske, Hans Triebel, Leszek Skrzypczak","submitted_at":"2023-10-20T15:06:14Z","abstract_excerpt":"The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished Besov spaces $B^s_p(\\mathbb{R}^n) = B^s_{p,p}(\\mathbb{R}^n)$, $1\\le p \\le \\infty$, and between Sobolev spaces $H^s_p(\\mathbb{R}^n)$, $1<p< \\infty$. In contrast to the paper {\\em H. Triebel, Mapping properties of Fourier transforms. Z. Anal. Anwend. 41 (2022), 133--152}, based mainly on embeddings between related weighted spaces, we rely on wavelet expansions, duality and interpolation of corresponding (unweighted) spaces, and (appropriately extended) Hausdorff-Young inequalities. The d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.13567","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/2310.13567/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"}