{"paper":{"title":"Some remarks on $L^1$ embeddings in the subelliptic setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Daniel Spector, Marco M. Peloso, Steven G. Krantz","submitted_at":"2019-06-05T09:13:41Z","abstract_excerpt":"In this paper we establish an optimal Lorentz estimate for the Riesz potential in the $L^1$ regime in the setting of a stratified group $G$: Let $Q\\geq 2$ be the homogeneous dimension of $G$ and $\\mathcal{I}_\\alpha$ denote the Riesz potential of order $\\alpha$ on $G$. Then, for every $\\alpha \\in (0,Q)$, there exists a constant $C=C(\\alpha,Q)>0$ such that \\begin{align} \\| \\mathcal{I}_\\alpha f \\|_{L^{Q/(Q-\\alpha),1}(G)} \\leq C\\| X \\mathcal{I}_1 f \\|_{L^1(G)} \\end{align} for distributions $f$ such that $X \\mathcal{I}_1 f \\in L^1(G)$, where $X$ denotes the horizontal gradient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01896","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"}