Carleson型极大算子的等价性与有界性  

The Equivalence and Boundedness of Carleson-Type Maximal Operator

作　　者：许珍惜[1] 刘红海[1] 

机构地区：[1]河南理工大学,河南焦作454000

出　　处：《焦作大学学报》2013年第4期85-87,共3页Journal of Jiaozuo University

摘　　要：Carleson型极大算子源于Fourier级数的点态收敛性研究,该算子与振荡奇异积分算子有密切的联系。在Carleson型极大算子的研究中出现了一些不同形式,文章首先将用线性化方法证明两类不同形式的Carleson型极大算子是相等的。其次,文章对于相函数为含有一次项的多项式的情形,将运用Calderon-Zygmund旋转方法证明带粗糙核的Carleson型极大算子LP是有界的,1<p<2.Carleson-type maximal operators derives from the research of Pointwis e convergence of Fourier progression. This operator has a close relationship with the oscillatory singular integral operators. There have been some different forms of Carleson-type maximal operator research, so the article will firstly use the linearization method to prove that two different forms of Carleson-type maximal operators are equal. Secondly, against the function that contains the case of a polynomial term, the article will use Calderon-Zygmund rotation method to prove Carleson-type maximal operator LP with rough kernel is bounded, 1<p<2.

关 键 词：Carleson型极大算子 粗糙核 振荡奇异积分 旋转方法 线性化方法 

分 类 号：O143[理学—数学]