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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.01256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T12:51:44Z","cross_cats_sorted":[],"title_canon_sha256":"773cf369756b46063907e7b99588d9d7d4dd5a098710f349aa62c049037bc085","abstract_canon_sha256":"c6bcffc74bcec3b2ef830778cfe9ee5f47e2de2d69275653b4b85ba701e5be31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:37.349066Z","signature_b64":"XkGrMPy9WPlnbnha6tRW5k7AyZ7BfUxu6LvnYr7z2dsJ5S46KSzDxhEx95oxreJqbnUJtupDMcmoyJp5MnJ4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9e04b49087c793b0bc8e2eeb50c928dc765a1665cf0f6973ae8a8d5d4929f6c","last_reissued_at":"2026-05-18T01:15:37.348340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:37.348340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb R_+:=(0,\\infty)$. 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