{"paper":{"title":"A new maximal regularity for parabolic equations and an application","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangying Lv, Jinlong Wei, Jinqiao Duan, Wei Wang","submitted_at":"2024-11-20T12:36:07Z","abstract_excerpt":"We introduce the Lebesgue--H\\\"{o}lder--Dini and Lebesgue--H\\\"{o}lder spaces $L^p(\\mathbb{R};{\\mathcal C}_{\\vartheta,\\varsigma}^{\\alpha,\\rho}({\\mathbb R}^n))$ ($\\vartheta\\in \\{l,b\\}, \\, \\varsigma\\in \\{d,s,c,w\\}$, $p\\in (1,+\\infty]$ and $\\alpha\\in [0,1)$), and then use a vector-valued Calder\\'{o}n--Zygmund theorem to establish the maximal Lebesgue--H\\\"{o}lder--Dini and Lebesgue--H\\\"{o}lder regularity for a class of parabolic equations. As an application, we obtain the unique strong solvability of the following stochastic differential equation \\begin{eqnarray*} X_{s,t}(x)=x+\\int\\limits_s^tb(r,X_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13266","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13266/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}