{"paper":{"title":"An $L^1$-type estimate for Riesz potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Armin Schikorra, Daniel Spector, Jean Van Schaftingen","submitted_at":"2014-11-10T04:28:56Z","abstract_excerpt":"In this paper we establish new $L^1$-type estimates for the classical Riesz potentials of order $\\alpha \\in (0, N)$: \\[\n  \\|I_\\alpha u\\|_{L^{N/(N-\\alpha)}(\\mathbb{R}^N)} \\leq C \\|Ru\\|_{L^1(\\mathbb{R}^N;\\mathbb{R}^N)}. \\] This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space $\\mathcal{H}^1(\\mathbb{R}^N)$ and provides a new family of $L^1$-Sobolev inequalities for the Riesz fractional gradient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2318","kind":"arxiv","version":4},"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"}