{"paper":{"title":"Riesz Transform Characterization and Fefferman-Stein Decomposition of Triebel-Lizorkin Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Qixiang Yang, Xing Fu","submitted_at":"2016-02-02T09:23:51Z","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, via an auxiliary function space $\\mathrm{WE}^{1,\\,q}(\\mathbb R^D)$ defined via wavelet expansions, the authors establish the Riesz transform characterization of Triebel-Lizorkin spaces $\\dot{F}^0_{1,\\,q}(\\mathbb{R}^D)$. As a consequence, the authors obtain the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $\\dot{F}^0_{\\infty,\\,q'}(\\mathbb{R}^D)$. Finally, the authors give an explicit example to show that $\\dot{F}^0_{1,\\,q}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00847","kind":"arxiv","version":2},"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"}