{"paper":{"title":"A characterization of Hardy spaces associated with certain Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jacek Dziuba\\'nski, Jacek Zienkiewicz","submitted_at":"2013-10-08T20:12:44Z","abstract_excerpt":"Let $\\{K_t\\}_{t>0}$ be the semigroup of linear operators generated by a Schr\\\"odinger operator $-L=\\Delta - V(x)$ on $\\mathbb R^d$, $d\\geq 3$, where $V(x)\\geq 0$ satisfies $\\Delta^{-1} V\\in L^\\infty$. We say that an $L^1$-function $f$ belongs to the Hardy space $H^1_L$ if the maximal function $\\mathcal M_L f(x) = \\sup_{t>0} |K_tf(x)|$ belongs to $L^1(\\mathbb R^d) $. We prove that the operator $(-\\Delta)^{1\\slash 2} L^{-1\\slash 2}$ is an isomorphism of the space $H^1_L$ with the classical Hardy space $H^1(\\mathbb R^d)$ whose inverse is $L^{1\\slash 2} (-\\Delta)^{-1\\slash 2}$. As a corollary we o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2262","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"}