A sparse estimate for multisublinear forms involving vector-valued maximal functions
A sparse estimate for multisublinear forms involving vector-valued maximal functions
复制标题
涉及向量值极大函数的多重次线性形式的稀疏估计
DOI：
10.6092/issn.2240-2829/8171
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Yumeng Ou
中科院分区：
文献类型：
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作者：
Amalia Culiuc;F. Plinio;Yumeng Ou
我们证明了一个稀疏界的$m$-次线性形式相关联的向量值极大函数的Festhiman-Stein型。作为结果，我们证明了多次线性算子的稀疏界通过$\ell^r$-值扩张得以保持。这一观察反过来又被用来推导向量值，多线性加权范数不等式的multissublinear运营商遵守稀疏的界限，这是遥不可及的外推理论最近开发的克鲁兹-乌里韦和马特尔。作为一个例子，利用作者的标量稀疏控制定理，得到了双线性Hilbert变换的向量值多线性加权不等式。
We prove a sparse bound for the $m$-sublinear form associated to vector-valued maximal functions of Fefferman-Stein type. As a consequence, we show that the sparse bounds of multisublinear operators are preserved via $\ell^r$-valued extension. This observation is in turn used to deduce vector-valued, multilinear weighted norm inequalities for multisublinear operators obeying sparse bounds, which are out of reach for the extrapolation theory recently developed by Cruz-Uribe and Martell. As an example, vector-valued multilinear weighted inequalities for bilinear Hilbert transforms are deduced from the scalar sparse domination theorem of the authors.