{"paper":{"title":"Weak factorization of the Hardy space $H^p$ for small values of $p$, in the multilinear setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Marie-Jose S. Kuffner","submitted_at":"2018-02-06T02:50:15Z","abstract_excerpt":"We give a weak factorization proof of the Hardy space $H^{p}(\\mathbb{R}^{n})$ in the multilinear setting, for $\\frac{n}{n+1} < p <1$. As a consequence, we obtain a characterization of the boundedness of the commutator $[b,T]$ from $L^{r_{1}}(\\mathbb R^n) \\text{~x ... x~} L^{r_{m}} (\\mathbb R^n) \\text{ to } L^{q^\\prime} (\\mathbb R^n)$, where $b \\in \\text{Lip}_\\alpha (\\mathbb R^n)$, and $\\frac{\\alpha}{n} = \\sum_{i=1}^{m} \\frac{1}{r_{i}} +\\frac{1}{q} - 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01768","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"}