{"paper":{"title":"A characterization of two weight norm inequality for Littlewood-Paley $g_{\\lambda}^{*}$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kangwei Li, Mingming Cao, Qingying Xue","submitted_at":"2015-04-29T13:17:53Z","abstract_excerpt":"Let $n\\ge 2$ and $g_{\\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, \\begin{align*} g_{\\lambda}^{*}(f)(x) =\\bigg(\\iint_{\\mathbb R^{n+1}_{+}} \\Big(\\frac{t}{t+|x-y|}\\Big)^{n\\lambda} |\\nabla P_tf(y,t)|^2 \\frac{dy dt}{t^{n-1}}\\bigg)^{1/2}, \\ \\quad \\lambda > 1, \\end{align*} where $P_tf(y,t)=p_t*f(y)$, $p_t(y)=t^{-n}p(y/t)$ and $p(x) = (1+|x|^2)^{-(n+1)/2}$, $\\nabla =(\\frac{\\partial}{\\partial y_1},\\ldots,\\frac{\\partial}{\\partial y_n},\\frac{\\partial}{\\partial t})$. In this paper, we give a characterization of two-weight norm ine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07850","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"}