{"paper":{"title":"Differentiability properties of Riesz potentials of finite measures and non-doubling Calder\\'on-Zygmund theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joan Verdera, Juli\\`a Cuf\\'i","submitted_at":"2016-05-11T11:38:13Z","abstract_excerpt":"We study differentiability properties of Riesz potentials of finite Borel measures in dimension d larger than 2. The Riesz kernel has homogeneity 2-d. In dimension 2 we consider logarithmic potentials. We introduce a notion of differentiability in the capacity sense, capacity being Newtonian capacity in dimension larger than 2 and Wiener capacity in the plane. It turns out that differentiability in the capacity sense at a point is related to the existence of principal values of the measure with respect to the vector valued Riesz potential x/|x|^d of homogeneity 1-d. This leads to Calder\\'on-Zy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03388","kind":"arxiv","version":3},"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"}