{"paper":{"title":"An atomic decomposition characterization of flag Hardy spaces $H^p_F({\\rr}^{n}\\times{\\rr}^m)$ with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Xinfeng Wu","submitted_at":"2012-10-20T16:29:36Z","abstract_excerpt":"In this paper, we give an atomic decomposition characterization of flag Hardy spaces $H^p_F({\\rr}^n\\times {\\rr}^m)$ for $0<p\\le 1$, which were introduced in \\cite{hl1}. A remarkable feature of atoms of such flag Hardy spaces is that these atoms have only partial cancellation conditions. As an application, we prove a boundedness criterion for operators on flag Hardy spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5641","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"}