A criterion on oscillation and variation for the commutators of singular integral operators
A criterion on oscillation and variation for the commutators of singular integral operators
复制标题
奇异积分算子换向器振荡和变差判据
DOI：
10.1515/forum-2012-0019
复制
发表时间：
2015-01-01
影响因子：
0.8
通讯作者：
Wu, Huoxiong
中科院分区：
文献类型：
--
作者：
Liu, Feng;Wu, Huoxiong
给出了1维Calderon-Zygmund奇异积分对易子的振荡算子和变分算子的加权范数估计的一个判据。作为应用，得到了Hilbert变换和hermite Riesz变换对易子的振荡算子和rho变分算子的加权l -p有界性。此外，还给出了lambda跳转算子的相应结果以及与这些算子相关的向上交叉次数。
This paper gives a criterion on the weighted norm estimates of the oscillatory and variation operators for the commutators of Calderon-Zygmund singular integrals in dimension 1. As applications, the weighted L-p-boundedness of the oscillation operators and the rho-variation operators for commutators of the Hilbert transform and the Hermitian Riesz transform are obtained. In addition, the corresponding results for the lambda-jump operators and the numbers of up-crossings associated with these operators are also given.