{"paper":{"title":"An $L_q(L_p)$-theory for parabolic pseudo-differential equations: Calder\\'on-Zygmund approach","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":"2015-03-16T04:42:22Z","abstract_excerpt":"In this paper we present a Calder\\'{o}n-Zygmund approach for a large class of parabolic equations with pseudo-differential operators $\\mathcal{A}(t)$ of arbitrary order $\\gamma\\in(0,\\infty)$. It is assumed that $\\cA(t)$ is merely measurable with respect to the time variable. The unique solvability of the equation $$ \\frac{\\partial u}{\\partial t}=\\cA u-\\lambda u+f, \\quad (t,x)\\in \\fR^{d+1} $$\n  and the $L_{q}(\\fR,L_{p})$-estimate $$ \\|u_{t}\\|_{L_{q}(\\fR,L_{p})}+\\|(-\\Delta)^{\\gamma/2}u\\|_{L_{q}(\\fR,L_{p})} +\\lambda\\|u\\|_{L_{q}(\\fR,L_{p})}\\leq N\\|f\\|_{L_{q}(\\fR,L_{p})} $$ are obtained for any $\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04521","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"}