{"paper":{"title":"Atomic decomposition of real-variable type for Bergman spaces in the unit ball of $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Wei Ouyang, Zeqian Chen","submitted_at":"2013-03-09T08:34:53Z","abstract_excerpt":"In this paper, we show that every (weighted) Bergman space $\\mathcal{A}^p_{\\alpha} (\\mathbb{B}_n)$ in the complex ball admits an atomic decomposition of real-variable type for any $0 < p \\le 1$ and $\\alpha > -1.$ More precisely, for each $f \\in \\mathcal{A}^p_{\\alpha} (\\mathbb{B}_n)$ there exist a sequence of real-variable $(p, \\8)_{\\alpha}$-atoms $a_k$ and a scalar sequence $\\{\\lambda_k \\}$ with $\\sum_k | \\lambda_k |^p < \\8$ such that $f = \\sum_k \\lambda_k P_{\\alpha} (a_k),$ where $P_{\\alpha}$ is the Bergman projection from $L^2_{\\alpha} (\\mathbb{B}_n)$ onto $\\mathcal{A}^2_{\\alpha} (\\mathbb{B}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2182","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"}