{"paper":{"title":"On The Boundedness of Bi-parameter Littlewood-Paley $g_{\\lambda}^{*}$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Mingming Cao, Qingying Xue","submitted_at":"2015-12-02T04:01:11Z","abstract_excerpt":"Let $m,n\\ge 1$ and $g_{\\lambda_1,\\lambda_2}^*$ be the bi-parameter Littlewood-Paley $g_{\\lambda}^{*}$-function defined by $$ g_{\\lambda_1,\\lambda_2}^*(f)(x)= \\bigg(\\iint_{\\R^{m+1}_{+}} \\big(\\frac{t_2}{t_2 + |x_2 - y_2|}\\big)^{m \\lambda_2} \\iint_{\\R^{n+1}_{+}} \\big(\\frac{t_1}{t_1 + |x_1 - y_1|}\\big)^{n \\lambda_1}|\\theta_{t_1,t_2} f(y_1,y_2)|^2 \\frac{dy_1 dt_1}{t_1^{n+1}} \\frac{dy_2 dt_2}{t_2^{m+1}} \\bigg)^{1/2}, \\lambda_1>1,\\quad \\lambda_2>1 $$ where $\\theta_{t_1,t_2} f$ is a non-convolution kernel defined on $\\mathbb{R}^{m+n}$. In this paper, we showed that the bi-parameter Littlewood-Paley fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00569","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"}