{"paper":{"title":"A parabolic Triebel-Lizorkin space estimate for the fractional Laplacian operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Minsuk Yang","submitted_at":"2016-06-03T17:07:50Z","abstract_excerpt":"In this paper we prove a parabolic Triebel-Lizorkin space estimate for the operator given by \\[T^{\\alpha}f(t,x) = \\int_0^t \\int_{{\\mathbb R}^d} P^{\\alpha}(t-s,x-y)f(s,y) dyds,\\] where the kernel is \\[P^{\\alpha}(t,x) = \\int_{{\\mathbb R}^d} e^{2\\pi ix\\cdot\\xi} e^{-t|\\xi|^\\alpha} d\\xi.\\] The operator $T^{\\alpha}$ maps from $L^{p}F_{s}^{p,q}$ to $L^{p}F_{s+\\alpha/p}^{p,q}$ continuously. It has an application to a class of stochastic integro-differential equations of the type $du = -(-\\Delta)^{\\alpha/2} u dt + f dX_t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01188","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"}