{"paper":{"title":"Embedding Theorems for M\\\"untz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dan Timotin, Emmanuel Fricain (ICJ), Isabelle Chalendar (ICJ)","submitted_at":"2010-01-18T10:43:15Z","abstract_excerpt":"We discuss boundedness and compactness properties of the embedding $M_\\Lambda^1\\subset L^1(\\mu)$, where $M_\\Lambda^1$ is the closure of the monomials $x^{\\lambda_n}$ in $L1([0,1])$ and $\\mu$ is a finite positive Borel measure on the interval $[0,1]$. In particular, we introduce a class of \"sublinear\" measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $\\Lambda$. Finally, we show how one can recapture some of Al Alam's results on boundedness and essential norm of weighted composition operators from $M_\\Lambda^1$ to $L1([0,1])$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3013","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"}