{"paper":{"title":"Atomic Characterizations of Hardy Spaces Associated to Schr\\\"{o}dinger Type Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Junqiang Zhang, Zongguang Liu","submitted_at":"2018-11-29T14:18:29Z","abstract_excerpt":"In this article, the authors consider the Schr\\\"{o}dinger type operator $L:=-{\\rm div}(A\\nabla)+V$ on $\\mathbb{R}^n$ with $n\\geq 3$, where the matrix $A$ is symmetric and satisfies uniformly elliptic condition and the nonnegative potential $V$ belongs to the reverse H\\\"{o}lder class $RH_q(\\mathbb{R}^n)$ with $q\\in(n/2,\\,\\infty)$. Let $p(\\cdot):\\ \\mathbb{R}^n\\to(0,\\,1]$ be a variable exponent function satisfying the globally $\\log$-H\\\"{o}lder continuous condition. The authors introduce the variable Hardy space $H_L^{p(\\cdot)}(\\mathbb{R}^n)$ associated to $L$ and establish its atomic characteriz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12820","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"}