{"paper":{"title":"The duality about function set and Fefferman-Stein Decomposition","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Qixiang Yang, Tao Qian","submitted_at":"2017-02-02T01:40:50Z","abstract_excerpt":"Let $D\\in\\mathbb{N}$, $q\\in[2,\\infty)$ and $(\\mathbb{R}^D,|\\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, the authors establish the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $\\dot{F}^0_{\\infty,\\,q'}(\\mathbb{R}^D)$ on basis of the dual on function set which has special topological structure. The function in Triebel-Lizorkin spaces $\\dot{F}^0_{\\infty,\\,q'}(\\mathbb{R}^D)$ can be written as the certain combination of $D+1$ functions in $\\dot{F}^0_{\\infty,\\,q'}(\\mathbb{R}^D) \\bigcap L^{\\infty}(\\mathbb{R}^D)$.\n  To get such deco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00520","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"}