{"paper":{"title":"Sharp Continuity Results for the Short-Time Fourier Transform and for Localization Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elena Cordero, Fabio Nicola","submitted_at":"2009-04-09T11:55:21Z","abstract_excerpt":"We completely characterize the boundedness on $L^p$ spaces and on Wiener amalgam spaces of the short-time Fourier transform (STFT) and of a special class of pseudodifferential operators, called localization operators. Precisely, a well-known STFT boundedness result on $L^p$ spaces is proved to be sharp. Then, sufficient conditions for the STFT to be bounded on the Wiener amalgam spaces $W(L^p,L^q)$ are given and their sharpness is shown. Localization operators are treated similarly. Using different techniques from those employed in the literature, we relax the known sufficient boundedness cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1508","kind":"arxiv","version":2},"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"}