Convex body domination and weighted estimates with matrix weights
Convex body domination and weighted estimates with matrix weights
复制标题
凸体支配和矩阵权重的加权估计
DOI：
10.1016/j.aim.2017.08.001
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发表时间：
2017
影响因子：
1.7
通讯作者：
A. Volberg
中科院分区：
文献类型：
--
作者：
F. Nazarov;S. Petermichl;S. Treil;A. Volberg
我们引入了所谓的凸体值稀疏算子，它将稀疏算子的概念推广到向量值函数空间。我们证明了Calderón-Zygmund算子以及Haar移位和仿积可以被这样的算子支配。通过估计稀疏算子，我们得到加权估计矩阵权重。我们得到了两个加权A2-A∞估计，在一个加权情形下给出了估计<$T <$L2（W）→ L2（W）≤ C [W] A2 1/2 [W] A∞≤ C [W] A2 3/2，其中T是Calderón-Zygmund算子（连续模满足Dini条件），或者是Haar移位或仿积.
We introduce the so called convex body valued sparse operators, which generalize the notion of sparse operators to the case of spaces of vector valued functions. We prove that Calderón–Zygmund operators as well as Haar shifts and paraproducts can be dominated by such operators. By estimating sparse operators we obtain weighted estimates with matrix weights. We get two weight A 2–A∞ estimates, that in the one weight case give us the estimate‖ T‖ L 2 (W)→ L 2 (W)≤ C [W] A 2 1/2 [W] A∞≤ C [W] A 2 3/2 where T is either Calderón–Zygmund operator (with modulus of continuity satisfying the Dini condition), or a Haar shift or a paraproduct.