{"paper":{"title":"Factorization in mixed norm Hardy and BMO spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Richard Lechner","submitted_at":"2016-10-05T16:22:05Z","abstract_excerpt":"Let $1\\leq p,q < \\infty$ and $1\\leq r \\leq \\infty$. We show that the direct sum of mixed norm Hardy spaces $\\big(\\sum_n H^p_n(H^q_n)\\big)_r$ and the sum of their dual spaces $\\big(\\sum_n H^p_n(H^q_n)^*\\big)_r$ are both primary. We do so by using Bourgain's localization method and solving the finite dimensional factorization problem. In particular, we obtain that the spaces $\\big(\\sum_{n\\in \\mathbb N} H_n^1(H_n^s)\\big)_r$, $\\big(\\sum_{n\\in \\mathbb N} H_n^s(H_n^1)\\big)_r$, as well as $\\big(\\sum_{n\\in \\mathbb N} BMO_n(H_n^s)\\big)_r$ and $\\big(\\sum_{n\\in \\mathbb N} H^s_n(BMO_n)\\big)_r$, $1 < s < \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01506","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"}