{"paper":{"title":"Analytic capacity and projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Alan Chang, Xavier Tolsa","submitted_at":"2017-12-02T11:56:04Z","abstract_excerpt":"In this paper we study the connection between the analytic capacity of a set and the size of its orthogonal projections. More precisely, we prove that if $E\\subset \\mathbb C$ is compact and $\\mu$ is a Borel measure supported on $E$, then the analytic capacity of $E$ satisfies $$ \\gamma(E) \\geq c\\,\\frac{\\mu(E)^2}{\\int_I \\|P_\\theta\\mu\\|_2^2\\,d\\theta}, $$ where $c$ is some positive constant, $I\\subset [0,\\pi)$ is an arbitrary interval, and $P_\\theta\\mu$ is the image measure of $\\mu$ by $P_\\theta$, the orthogonal projection onto the line $\\{re^{i\\theta}:r\\in\\mathbb R\\}$. This result is related to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00594","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"}