论文标题
稀疏的统治意味着矢量值稀疏统治
Sparse domination implies vector-valued sparse domination
论文作者
论文摘要
我们证明，多线性操作员的标量值稀疏统治意味着对于准巴纳赫函数空间的载体值稀疏统治，为此我们引入了UMD条件的多线性类似物。该条件的特征是多公共性硬木极限最大操作员的界限，并且超出了在每个单个空间上假定UMD条件的示例，包括例如迭代的Lebesgue，Lorentz和Orlicz空间。我们的方法使我们能够直接从标量价稀疏的统治中获得尖锐的矢量值加权边界，而无需使用卢比奥·德弗朗西亚（Rubio de Francia）型外推结果。 我们将结果应用于多线性Calderón-Zygmund操作员的新矢量值界限，并以新的尖锐的加权结合恢复了旧的载体。此外，在Banach函数空间设置中，我们对双线性希尔伯特变换的最新矢量值界限进行了改进。
We prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition is characterized by the boundedness of the multisublinear Hardy-Littlewood maximal operator and goes beyond examples in which a UMD condition is assumed on each individual space and includes e.g. iterated Lebesgue, Lorentz, and Orlicz spaces. Our method allows us to obtain sharp vector-valued weighted bounds directly from scalar-valued sparse domination, without the use of a Rubio de Francia type extrapolation result. We apply our result to obtain new vector-valued bounds for multilinear Calderón-Zygmund operators as well as recover the old ones with a new sharp weighted bound. Moreover, in the Banach function space setting we improve upon recent vector-valued bounds for the bilinear Hilbert transform.
