{"paper":{"title":"Parabolic BMO estimates for pseudo-differential operators of arbitrary order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim","submitted_at":"2014-08-11T08:06:30Z","abstract_excerpt":"In this article we prove the BMO-$L_{\\infty}$ estimate $$ \\|(-\\Delta)^{\\gamma/2} u\\|_{BMO(\\mathbf{R}^{d+1})}\\leq N \\|\\frac{\\partial}{\\partial t}u-A(t)u\\|_{L_{\\infty}(\\mathbf{R}^{d+1})}, \\quad \\forall\\, u\\in C^{\\infty}_c(\\mathbf{R}^{d+1}) $$ for a wide class of pseudo-differential operators $A(t)$ of order $\\gamma\\in (0,\\infty)$. The coefficients of $A(t)$ are assumed to be merely measurable in time variable. As an application to the equation $$ \\frac{\\partial}{\\partial t}u=A(t)u+f,\\quad t\\in \\mathbf{R} $$ we prove that for any $u\\in C^{\\infty}_c(\\mathbf{R}^{d+1})$ $$ \\|u_t\\|_{L_p(\\mathbf{R}^{d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2343","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"}