{"paper":{"title":"$L^p$ estimates for an oscillating Dunkl multiplier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B\\'echir Amri, Mohamed Gaidi","submitted_at":"2017-03-05T14:31:19Z","abstract_excerpt":"In this paper, we study the $L^p$ boundedness of a class of oscillating multiplier operator for the Dunkl transform, $T_{m_\\alpha}=\\mathcal{F}_k^{-1}(m_{\\alpha}\\mathcal{F}_k(f))$ with $m(\\xi)=|\\xi|^{-\\alpha}e^{\\pm i|\\xi|}\\phi(\\xi)$. We obtain an $L^p$-bound result for the corresponding maximal functions. As a specific applications, we give an extension of the $L^p$ estimate for the wave equation and of Stein's theorem for the analytic family of maximal spherical means \\cite{Stein}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01600","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"}