{"paper":{"title":"Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Dongyong Yang, Ji Li, Xuan Thinh Duong","submitted_at":"2015-08-31T21:24:14Z","abstract_excerpt":"Fix $\\lambda>0$. Consider the Hardy space $H^1(\\mathbb{R}_+,dm_\\lambda)$ in the sense of Coifman and Weiss, where $\\mathbb{R_+}:=(0,\\infty)$ and $dm_\\lambda:=x^{2\\lambda}dx$ with $dx$ the Lebesgue measure. Also consider the Bessel operators $\\Delta_\\lambda:=-\\frac{d^2}{dx^2}-\\frac{2\\lambda}{x} \\frac d{dx}$, and $S_\\lambda:=-\\frac{d^2}{dx^2}+\\frac{\\lambda^2-\\lambda}{x^2}$ on $\\mathbb{R_+}$. The Hardy spaces $H^1_{\\Delta_\\lambda}$ and $H^1_{S_\\lambda}$ associated with $\\Delta_\\lambda$ and $S_\\lambda$ are defined via the Riesz transforms $R_{\\Delta_\\lambda}:=\\partial_x (\\Delta_\\lambda)^{-1/2}$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00079","kind":"arxiv","version":2},"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"}