{"paper":{"title":"Hardy spaces for Bessel-Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Edyta Kania, Marcin Preisner","submitted_at":"2016-03-23T13:53:42Z","abstract_excerpt":"Consider the Bessel operator with a potential on L^2((0,infty), x^a dx), namely Lf(x) = -f\"(x) - a/x f'(x) + V(x)f(x). We assume that a>0 and V\\in L^1_{loc}((0,infty), x^a dx) is a non-negative function. By definition, a function f\\in L^1((0,infty), x^a dx) belongs to the Hardy space H^1(L) if sup_{t>0} |e^{-tL} f| \\in L^1((0,infty), x^a dx). Under certain assumptions on V we characterize the space H^1(L) in terms of atomic decompositions of local type. In the second part we prove that this characterization can be applied to L for a \\in (0,1) with no additional assumptions on the potential V."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07685","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"}