{"paper":{"title":"Oscillation and variation for semigroups 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":"2016-05-04T12:51:44Z","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 ${\\mathcal O(P^{[\\lambda]}_\\ast)}$ and variation operator ${\\mathcal V}_\\rho(P^{[\\lambda]}_\\ast)$ of the Poisson semigroup $\\{P^{[\\lambda]}_t\\}_{t>0}$ associated with $\\Delta_\\lambda$ are both bounded on $L^p(\\mathbb R_+, dm_\\lambda)$ for $p\\in(1, \\infty)$, $BMO({{\\mathbb R}_+},dm_\\lambda)$, from $L^1({{\\mathbb R}_+},dm_\\lambda)$ to $L^{1,\\,\\infty}({{\\mathbb R}_+},dm_\\lambda)$, and from $H^1({{\\mathbb R}_+},dm_\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01256","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"}