论文标题
多线性利特伍德 - 帕利操作员的弱和强类型估计
Weak and strong type estimates for the multilinear Littlewood-Paley operators
论文作者
论文摘要
令$s_α$为圆锥上定义的多线性正方形函数，并用孔径$α\ geq 1 $。在本文中，我们研究了几种$s_α$的加权规范不等式。我们首先根据光圈$α$和$ \ vec {w} \在_ {\ vec {p}} $中获得尖锐的加权估计。通过一些重点的估计，我们还建立了两次重量不等式，包括凸起和熵凸起估计，以及具有任意权重的Fefferman-Stein不平等现象。除此之外，我们考虑了相应的索耶的混合类型估计值，为此，Coifman-Fefferman的不平等现象具有精确的$ a _ {\ infty} $ norm。最后，我们分别使用外推技术和二元分析提出了局部衰减估计。 Littlewood-Paley $ g^*_λ$函数的上述所有结论。即使在线性情况下，有些结果也是新的。
Let $S_α$ be the multilinear square function defined on the cone with aperture $α\geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_α$. We first obtain a sharp weighted estimate in terms of aperture $α$ and $\vec{w} \in A_{\vec{p}}$. By means of some pointwise estimates, we also establish two-weight inequalities including bump and entropy bump estimates, and Fefferman-Stein inequalities with arbitrary weights. Beyond that, we consider the mixed weak type estimates corresponding Sawyer's conjecture, for which a Coifman-Fefferman inequality with the precise $A_{\infty}$ norm is proved. Finally, we present the local decay estimates using the extrapolation techniques and dyadic analysis respectively. All the conclusions aforementioned hold for the Littlewood-Paley $g^*_λ$ function. Some results are new even in the linear case.
