论文标题
多线粗糙的单数积分运算符
Multilinear rough singular integral operators
论文作者
论文摘要
我们研究$ m $ - 线性均质的粗糙单数积分运算符$ \ mathcal {l}_Ω$与intemable函数相关联$ \ mathbb {s}^{mn-1} $，平均值零。我们从$ l^{p_1} \ times \ cdots \ cdots \ times l^{p_m} $ to $ l^p $ $ l^{p_1} \ cdots \ cdots \ cd { $ω\ in l^q（\ Mathbb s^{Mn-1}）$和$ q \ ge 2 $。该集合可以由$ \ mathbb r^m $中的凸多面体描述。
We study $m$-linear homogeneous rough singular integral operators $\mathcal{L}_Ω$ associated with integrable functions $Ω$ on $\mathbb{S}^{mn-1}$ with mean value zero. We prove boundedness for $\mathcal{L}_Ω$ from $L^{p_1}\times \cdots \times L^{p_m}$ to $L^p$ when $1<p_1,\dots, p_m<\infty$ and $1/p=1/p_1+\cdots +1/p_m$ in the largest possible open set of exponents when $Ω\in L^q(\mathbb S^{mn-1})$ and $q\ge 2$. This set can be described by a convex polyhedron in $\mathbb R^m$.
