{"paper":{"title":"On characterization of Poisson integrals of Schr\\\"odinger operators with Morrey traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liang Song, Lixin Yan, Xiaoxiao Tian","submitted_at":"2015-06-17T08:31:08Z","abstract_excerpt":"Let $L$ be a Schr\\\"odinger operator of the form $L=-\\Delta+V$ acting on $L^2(\\mathbb R^n)$ where the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_q$ for some $q\\geq n.$ In this article we will show that a function $f\\in L^{2, \\lambda}({\\mathbb{R}^n}), 0<\\lambda<n$ is the trace of the solution of ${\\mathbb L}u=-u_{tt}+L u=0, u(x,0)= f(x),$ where $u$ satisfies a Carleson type condition \\begin{eqnarray*}\n  \\sup_{x_B, r_B} r_B^{-\\lambda}\\int_0^{r_B}\\int_{B(x_B, r_B)} t|\\nabla u(x,t)|^2 {dx dt} \\leq C <\\infty. \\end{eqnarray*} Its proof heavily relies on investigate the intrins"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05239","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"}