{"paper":{"title":"Non-existence of reflectionless measures for the s-Riesz transform when 0<s<1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Laura Prat, Xavier Tolsa","submitted_at":"2015-02-05T10:06:50Z","abstract_excerpt":"A measure $\\mu$ on $\\mathbb{R}^d$ is called reflectionless for the $s$-Riesz transform if the singular integral $R^s\\mu(x)=\\int \\frac{y-x}{|y-x|^{s+1}}\\,d\\mu(y)$ is constant on the support of $\\mu$ in some weak sense and, moreover, the operator defined by $R^s_\\mu(f)=R^s(f\\,\\mu)$ is bounded in $L^2(\\mu)$. In this paper we show that the only reflectionless measure for the $s$-Riesz transform is the zero measure when $0<s<1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01483","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"}