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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.03952","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-10T14:07:11Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b36a0a1767b1f6cb488ae7cc8d55055a36b2f341aac4f437db9014574d6ac845","abstract_canon_sha256":"b85997a5ac66552a2ea872e2d0de471d9e48cdb2cc51f76f1dccf165305e0708"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:30.795725Z","signature_b64":"0k58MukVGXdGkX7TDK7mAp31yGDp7UBdgYJR63y0JyJd3TqhN06tySmBqbT22DZC6/0430YA25I2eOTOAkbgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06d5fa3c6523fb59d0a911a8b856c9567fb2b892f10fd0651420eda3b47273d5","last_reissued_at":"2026-05-18T00:00:30.795159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:30.795159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb{R}^{n}$. 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