{"paper":{"title":"Riesz transform characterization of Hardy spaces associated with Schr\\\"odinger operators with compactly supported potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jacek Dziuba\\'nski, Marcin Preisner","submitted_at":"2009-10-06T14:25:29Z","abstract_excerpt":"Let L=-\\Delta+V be a Schr\\\"odinger operator on R^d, d\\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semigroup generated by -L. We say that an L^1(R^d)-function f belongs to the Hardy space H_L^1 associated with L if sup_{t>0} |K_t f| belongs to L^1(R^d). We prove that f\\in H_L^1 if and only if R_j f \\in L^1(R^d) for j=1,...,d, where R_j= \\frac{d}{dx_j} L^{-1/2} are the Riesz transforms associated with L."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1017","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"}