{"paper":{"title":"Atomic decompositions for Hardy spaces related to Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Marcin Preisner","submitted_at":"2014-09-16T12:46:38Z","abstract_excerpt":"Let L_U = -Delta+U be a Schr\\\"odinger operator on R^d, where U\\in L^1_{loc}(R^d) is a non-negative potential and d\\geq 3. The Hardy space H^1(L_U) is defined in terms of the maximal function for the semigroup K_{t,U} = exp(-t L_U), namely H^1(L_U) = {f\\in L^1(R^d): \\|f\\|_{H^1(L_U)}:= \\|sup_{t>0} |K_{t,U} f| \\|_{L^1(R^d)} < \\infty. Assume that U=V+W, where V\\geq 0 satisfies the global Kato condition sup_{x\\in R^d} \\int_{R^d} V(y)|x-y|^{2-d} < \\infty. We prove that, under certain assumptions on W\\geq 0, the space H^1(L_U) admits an atomic decomposition of local type. An atom a for H^1(L_U) is ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4612","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"}