{"paper":{"title":"Weak factorization of Hardy spaces in the Bessel setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Roc Oliver","submitted_at":"2016-04-08T17:39:45Z","abstract_excerpt":"We provide the weak factorization of the Hardy spaces $H^{p}(\\mathbb{R}_+, dm_{\\lambda})$ in the Bessel setting, for $p\\in \\left(\\frac{2\\lambda + 1}{2\\lambda + 2}, 1\\right]$. As a corollary we obtain a characterization of the boundedness of the commutator $[b, R_{\\Delta_{\\lambda}}]$ from $L^{q}(\\mathbb{R}_+, dm_{\\lambda})$ to $L^{r}(\\mathbb{R}_+, dm_{\\lambda})$ when $b\\in \\textrm{Lip}_{\\alpha}(\\mathbb{R}_+, dm_{\\lambda})$ provided that $\\alpha = \\frac{1}{q} - \\frac{1}{r}$. The results are a slight generalization and modification of the work of Duong, Li, Yang, and the second named author, whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02409","kind":"arxiv","version":3},"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"}