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Let ${BMO}_{\\Delta_{N}}(\\mathbb R^n)$ denote the BMO space on $\\mathbb R^n$ associated to the Neumann operator $\\L$. In this article we will show that a function $f\\in { BMO}_{\\Delta_{N}}(\\mathbb R^n)$ is the trace of the solution of $${\\mathbb L}u=u_{t}+L u=0, u(x,0)= f(x),$$\n  where $u$ satisfies a Carleson-type condition \\begin{eqnarray*}\n  \\sup_{x_B, r_B} r_B^{-n}\\int_0^{r_B^2}\\int_{B(x_B, r_B)} |\\nabla u(x,t)|^2 {dx dt } \\leq C <\\infty, \\end{eqnarray*} for some constant $C>0$. Conversely, this Carleson","authors_text":"Chao Zhang, Minghua Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-13T04:31:00Z","title":"Application BMO type space to parabolic equations of Navier-Stokes type with the Neumann boundary condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04613","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:eb248e28014512a539f74b7b60937b39ad338f09b89235b8a3c3e95dc35735d4","target":"record","created_at":"2026-05-18T00:00:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d0f378817ad2249b72157a0a7a52e6bd34a7e4b9bc00512a623b2fe7e8806398","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-13T04:31:00Z","title_canon_sha256":"56560658b063e358c1503cf1169e631ae1e5948f36d2a4d15bf2a442911287b2"},"schema_version":"1.0","source":{"id":"1803.04613","kind":"arxiv","version":2}},"canonical_sha256":"f9d3b06199521119d34a40b423b745fb5be11972b75d80fe71030939837baef2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d3b06199521119d34a40b423b745fb5be11972b75d80fe71030939837baef2","first_computed_at":"2026-05-18T00:00:37.517021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:37.517021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nx2cf83Clf8D8Ms3anyDGbk/VNZy6krfwM5+ZenSKkyyQMGEKX+GUcR5lqakYAMkIL2v9L1aVvKmE1A0yGnRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:37.517570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04613","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb248e28014512a539f74b7b60937b39ad338f09b89235b8a3c3e95dc35735d4","sha256:201b4839ea0eb75862eadfa1fbf36bd0290792404cc24b632b126311efdd3953"],"state_sha256":"58a43bfbad24efdb9cb6916416edcdb392a097f696ef169e8acf4bb18f4b3b68"}