{"paper":{"title":"Capacities associated with Calder\\'on-Zygmund kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joan Mateu, Laura Prat, Vasilis Chousionis, Xavier Tolsa","submitted_at":"2011-12-16T15:26:11Z","abstract_excerpt":"Analytic capacity is associated with the Cauchy kernel $1/z$ and the $L^\\infty$-norm. For $n\\in\\mathbb{N}$, one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x|^{2n}$, $1\\le i\\le 2$, $x=(x_1,x_2)\\in\\mathbb{R}^2$. The main result of this paper states that the capacities associated with the vectorial kernel $(K_1, K_2)$ are comparable to analytic capacity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3849","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"}