{"paper":{"title":"Spectral multiplier theorems of Euclidean type on new classes of 2-step stratified groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Alessio Martini, Detlef M\\\"uller","submitted_at":"2013-06-03T12:52:48Z","abstract_excerpt":"From a theorem of Christ and Mauceri and Meda it follows that, for a homogeneous sublaplacian $L$ on a $2$-step stratified group $G$ with Lie algebra $\\mathfrak{g}$, an operator of the form $F(L)$ is of weak type $(1,1)$ and bounded on $L^p(G)$ for $1 < p < \\infty$ if the spectral multiplier $F$ satisfies a scale-invariant smoothness condition of order $s > Q/2$, where $Q = \\dim \\mathfrak{g} + \\dim[\\mathfrak{g},\\mathfrak{g}]$ is the homogeneous dimension of $G$. Here we show that the condition can be pushed down to $s > d/2$, where $d = \\dim \\mathfrak{g}$ is the topological dimension of $G$, p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0387","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"}