{"paper":{"title":"Hardy spaces associated with Schrodinger operators on the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chin-Cheng Lin, Heping Liu, Yu Liu","submitted_at":"2011-06-24T12:58:58Z","abstract_excerpt":"Let $L= -\\Delta_{\\mathbb{H}^n}+V$ be a Schr\\\"odinger operator on the Heisenberg group $\\mathbb{H}^n$, where $\\Delta_{\\mathbb{H}^n}$ is the sub-Laplacian and the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_{\\frac{Q}{2}}$ and $Q$ is the homogeneous dimension of $\\mathbb{H}^n$. The Riesz transforms associated with the Schr\\\"odinger operator $L$ are bounded from $L^1(\\mathbb{H}^n)$ to $L^{1,\\infty}(\\mathbb{H}^n)$. The $L^1$ integrability of the Riesz transforms associated with $L$ characterizes a certain Hardy type space denoted by $H^1_L(\\mathbb{H}^n)$ which is larger than "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4960","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"}