{"paper":{"title":"Oscillation and variation for Riesz transform associated with Bessel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyong Yang, Huoxiong Wu, Jing Zhang","submitted_at":"2016-05-04T12:44:52Z","abstract_excerpt":"Let $\\lambda>0$ and $\\triangle_\\lambda:=-\\frac{d^2}{dx^2}-\\frac{2\\lambda}{x} \\frac d{dx}$ be the Bessel operator on $\\mathbb R_+:=(0,\\infty)$. We show that the oscillation operator $\\mathcal{O}(R_{\\Delta_{\\lambda},\\ast})$ and variation operator $\\mathcal{V}_{\\rho}(R_{\\Delta_{\\lambda},\\ast})$ of the Riesz transform $R_{\\Delta_{\\lambda}}$ associated with\n  $\\Delta_\\lambda$ are both bounded on $L^p(\\mathbb R_+, dm_{\\lambda})$ for $p\\in(1,\\,\\infty)$, from $L^1(\\mathbb{R}_{+},dm_{\\lambda})$ to $L^{1,\\,\\infty}(\\mathbb{R}_{+},dm_{\\lambda})$, and from $L^{\\infty}(\\mathbb{R}_{+},dm_{\\lambda})$ to $BMO("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01251","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"}