{"paper":{"title":"Morrey spaces for Schr\\\"odinger operators with nonnegative potentials, fractional integral operators and the Adams inequality on the Heisenberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hua Wang","submitted_at":"2019-07-04T03:51:40Z","abstract_excerpt":"Let $\\mathcal L=-\\Delta_{\\mathbb H^n}+V$ be a Schr\\\"odinger operator on the Heisenberg group $\\mathbb H^n$, where $\\Delta_{\\mathbb H^n}$ is the sublaplacian on $\\mathbb H^n$ and the nonnegative potential $V$ belongs to the reverse H\\\"older class $RH_s$ with $s\\in[Q/2,\\infty)$. Here $Q=2n+2$ is the homogeneous dimension of $\\mathbb H^n$. For given $\\alpha\\in(0,Q)$, the fractional integral operator associated with the Schr\\\"odinger operator $\\mathcal L$ is defined by $\\mathcal I_{\\alpha}={\\mathcal L}^{-{\\alpha}/2}$. In this article, the author introduces the Morrey space $L^{p,\\kappa}_{\\rho,\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03573","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"}