{"paper":{"title":"Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Daniel Li (LML), Herv\\'e Queff\\'elec (LPP), Luis Rodriguez-Piazza","submitted_at":"2012-06-06T10:57:27Z","abstract_excerpt":"We prove that, for every $\\alpha > -1$, the pull-back measure $\\phi ({\\cal A}_\\alpha)$ of the measure $d{\\cal A}_\\alpha (z) = (\\alpha + 1) (1 - |z|^2)^\\alpha \\, d{\\cal A} (z)$, where ${\\cal A}$ is the normalized area measure on the unit disk $\\D$, by every analytic self-map $\\phi \\colon \\D \\to \\D$ is not only an $(\\alpha + 2)$-Carleson measure, but that the measure of the Carleson windows of size $\\eps h$ is controlled by $\\eps^{\\alpha + 2}$ times the measure of the corresponding window of size $h$. This means that the property of being an $(\\alpha + 2)$-Carleson measure is true at all infinit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1178","kind":"arxiv","version":1},"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"}