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Weak (1,1) boundedness for the higher order Christ-Journ'e commutator
LAI Xudong,DING Yong * #
School of Mathematical Sciences, Beijing Normal University, Beijing 100875
*Correspondence author
#Submitted by
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Funding: National Natural Science Foundation of China（No.11371057, 11471033, 11571160）, China Scholarship Council （No.201506040129）, Fundamental Research Funds for the Central Universities（No.2014KJJCA10）, Specialized Research Fund for the Doctoral Program（No.20130003110003）
Opened online: 4 November 2016
Accepted by: none
Citation: LAI Xudong,DING Yong.Weak (1,1) boundedness for the higher order Christ-Journ'e commutator[OL]. [ 4 November 2016] http://en.paper.edu.cn/en_releasepaper/content/4708655
 
 
A weak type $(1,1)$ estimate is established for the high order commutator introduced by Christ and Journ'e which is defined by[ T[a_1,cdots,a_l]f(x)=pv int K(x-y)(prod_{i=1}^lm_{x,y}a_i)cdot f(y)dy, ]where $m_{x,y}a_i=int_0^1a_i(sx+(1-s)y)ds$ and $K$ is the Calder'on-Zygmund convolution kernel on $mathbb{R}^d (dgeq2)$.
Keywords:higher order, Christ-Journ'e commutator, Calder'on-Zygmund convolution kernel,weak (1,1) boundedness.
 
 
 

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