{"paper":{"title":"Radial Fourier Multipliers in $\\mathbb{R}^3$ and $\\mathbb{R}^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Laura Cladek","submitted_at":"2016-10-11T05:54:35Z","abstract_excerpt":"We prove that for radial Fourier multipliers $m: \\mathbb{R}^3\\to\\mathbb{C}$ supported compactly away from the origin, $T_m$ is restricted strong type (p,p) if $K=\\hat{m}$ is in $L^p(\\mathbb{R}^3)$, in the range $1<p<\\frac{13}{12}$. We also prove an $L^p$ characterization for radial Fourier multipliers in four dimensions; namely, for radial Fourier multipliers $m: \\mathbb{R}^4\\to\\mathbb{C}$ supported compactly away from the origin, $T_m$ is bounded on $L^p(\\mathbb{R}^4)$ if and only if $K=\\hat{m}$ is in $L^p(\\mathbb{R}^4)$, in the range $1<p<\\frac{36}{29}$. Our method of proof relies on a geome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03201","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"}