{"paper":{"title":"On the bilinear square Fourier multiplier operators and related multilinear square functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kozo Yabuta, Qingying Xue, Zengyan Si","submitted_at":"2016-04-19T14:11:09Z","abstract_excerpt":"Let $n\\ge 1$ and $\\mathfrak{T}_{m}$ be the bilinear square Fourier multiplier operator associated with a symbol $m$, which is defined by $$ \\mathfrak{T}_{m}(f_1,f_2)(x) = \\biggl( \\int_{0}^\\infty\\Big|\\int_{(\\mathbb{R}^n)^2} e^{2\\pi ix\\cdot (\\xi_1 +\\xi_2) }m(t\\xi_1,t\\xi_2) \\hat{f}_{1}(\\xi_1)\\hat{f}_{2}(\\xi_2)d\\xi_1 d\\xi_2\\Big|^2\\frac{dt}{t } \\biggr)^{\\frac 12}. $$ Let $s$ be an integer with $s\\in[n+1,2n]$ and $p_0$ be a number satisfying $2n/s\\le p_0\\le 2$. Suppose that $\\nu_{\\vec{\\omega}}=\\prod_{i=1}^2\\omega_i^{p/ p_i}$ and each $\\omega_i$ is a nonnegative function on $\\mathbb{R}^n$. In this pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05579","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"}