{"paper":{"title":"H\\\"ormander's multiplier theorem for the Dunkl transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Agnieszka Hejna, Jacek Dziuba\\'nski","submitted_at":"2018-07-07T09:59:10Z","abstract_excerpt":"For a normalized root system $R$ in $\\mathbb R^N$ and a multiplicity function $k\\geq 0$ let $\\mathbf N=N+\\sum_{\\alpha \\in R} k(\\alpha)$. Denote by $dw(\\mathbf x)=\\prod_{\\alpha\\in R}|\\langle \\mathbf x,\\alpha\\rangle|^{k(\\alpha)}\\, d\\mathbf x $ the associated measure in $\\mathbb R^N$. Let $\\mathcal F$ stands for the Dunkl transform. Given a bounded function $m$ on $\\mathbb R^N$, we prove that if there is $s>\\mathbf N$ such that $m$ satisfies the classical H\\\"ormander condition with the smoothness $s$, then the multiplier operator $\\mathcal T_mf=\\mathcal F^{-1}(m\\mathcal Ff)$ is of weak type $(1,1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02640","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"}