{"paper":{"title":"Characterization of temperatures associated to Schr\\\"odinger operators with initial data in Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Chao Zhang, Qiang Huang","submitted_at":"2017-12-10T14:07:11Z","abstract_excerpt":"Let $\\mathcal{L}$ be a Schr\\\"odinger operator of the form $\\mathcal{L} = -\\Delta+V$ acting on $L^2(\\mathbb R^n)$ where the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_q$ for some $q\\geq n.$ Let $L^{p,\\lambda}(\\mathbb{R}^{n})$, $0\\le \\lambda<n$ denote the Morrey space on $\\mathbb{R}^{n}$. In this paper, we will show that a function $f\\in L^{2,\\lambda}(\\mathbb{R}^{n})$ is the trace of the solution of ${\\mathbb L}u=u_{t}+{\\mathcal{L}}u=0, u(x,0)= f(x),$ where $u$ satisfies a Carleson-type condition \\begin{eqnarray*} \\sup_{x_B, r_B} r_B^{-\\lambda}\\int_0^{r_B^2}\\int_{B(x_B, r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03952","kind":"arxiv","version":3},"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"}