{"paper":{"title":"Parabolic Littlewood-Paley inequality for $\\phi(-\\Delta)$-type operators and applications to Stochastic integro-differential equations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Panki Kim","submitted_at":"2013-02-20T18:01:49Z","abstract_excerpt":"In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type $\\phi(-\\Delta)$, where $\\phi$ is a Bernstein function. As an application, we construct an $L_p$-theory for the stochastic integro-differential equations of the type $du=(-\\phi(-\\Delta)u+f)dt +gdW_t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5053","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"}