{"paper":{"title":"Sharp estimates of unimodular Fourier multipliers on Wiener amalgam spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guoping Zhao, Weichao Guo","submitted_at":"2018-07-02T09:02:05Z","abstract_excerpt":"We study the boundedness on the Wiener amalgam spaces $W^{p,q}_s$ of Fourier multipliers with symbols of the type $e^{i\\mu(\\xi)}$, for some real-valued functions $\\mu(\\xi)$ whose prototype is $|\\xi|^{\\beta}$ with $\\beta\\in (0,2]$. Under some suitable assumptions on $\\mu$, we give the characterization of $W^{p,q}_s\\rightarrow W^{p,q}$ boundedness of $e^{i\\mu(D)}$, for arbitrary pairs of $0< p,q\\leq \\infty$. Our results are an essential improvement of the previous known results, for both sides of sufficiency and necessity, even for the special case $\\mu(\\xi)=|\\xi|^{\\beta}$ with $1<\\beta<2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00540","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"}