{"paper":{"title":"Characterizations for inner functions in certain function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Atte Reijonen, Toshiyuki Sugawa","submitted_at":"2018-01-30T02:48:32Z","abstract_excerpt":"For $\\frac12<p<\\infty$, $0<q<\\infty$ and a certain two-sided doubling weight $\\omega$, we characterize those inner functions $\\Theta$ for which $$\\|\\Theta'\\|_{A^{p,q}_\\omega}^q=\\int_0^1 \\left(\\int_0^{2\\pi} |\\Theta'(re^{i\\theta})|^p d\\theta\\right)^{q/p}\n  \\omega(r)\\,dr<\\infty.$$ Then we show a modified version of this result for $p\\ge q$. Moreover, two additional characterizations for inner functions whose derivative belongs to the Bergman space $A_\\omega^{p,p}$ are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09832","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"}