{"paper":{"title":"Boundedness of Bi-parameter Littlewood-Paley operators on product Hardy space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Qingying Xue, Zhengyang Li","submitted_at":"2016-05-02T13:32:10Z","abstract_excerpt":"Let $n_1,n_2\\ge 1, \\lambda_1>1$ and $\\lambda_2>1$. For any $x=(x_1,x_2) \\in \\mathbb {R}^n\\times\\mathbb{R}^m$, let $g$ and $g_{\\vec{\\lambda}}^*$ be the bi-parameter Littlewood-Paley square functions defined by \\begin{align*} g(f)(x)= \\Big(\\int_0^{\\infty}\\int_0^{\\infty}|\\theta_{t_1,t_2} f(x_1,x_2)|^2 \\frac{dt_1}{t_1} \\frac{dt_2}{t_2} \\Big)^{1/2}, \\hbox{and} \\end{align*} $$ g_{\\vec{\\lambda}}^*(f)(x) = \\Big(\\iint_{\\mathbb{R}^{m+1}_{+}} \\iint_{\\mathbb{R}^{n+1}_{+}} \\prod_{i=1}^2\\Big(\\frac{t_1}{t_i + |x_i - y_i|}\\Big)^{n_i \\lambda_i} |\\theta_{t_1,t_2} f(y_1,y_2)|^2 \\frac{dy_1 dt_1}{t_1^{n+1}} \\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00476","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"}