{"paper":{"title":"Hadamard gap series in weighted-type spaces on the unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Bingyang Hu, Songxiao Li","submitted_at":"2015-08-29T16:41:34Z","abstract_excerpt":"We give a sufficient and necessary condition for an analytic function $f(z)$ on the unit ball $\\BB$ in $\\CC^n$ with Hadamard gaps, that is, for $f(z)=\\sum_{k=1}^\\infty P_{n_k}(z)$ where $P_{n_k}(z)$ is a homogeneous polynomial of degree $n_k$ and $n_{k+1}/n_k \\ge c>1$ for all $k \\in \\NN$, to belong to the weighted-type space $H^\\infty_\\mu$ and the corresponding little weighted-type space $H^\\infty_{\\mu, 0}$, under some condition posed on the weighted funtion $\\mu$. We also study the growth rate of those functions in $H^\\infty_\\mu$. Finally, we characterize the boundedness and compactness of we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07475","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"}