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A Parabolic Singular Integral Operator With Rough Kernel
Yanping Chen 1,Yong Ding 2 * #,Dashan Fan 3
1.University of Science and Technology Beijing
2.Beijing Normal University
3.University of Wisconsin-Milwaukee， USA
*Correspondence author
#Submitted by
Subject:
Funding: 国家自然科学基金,教育部博士点基金（No.10571015,20050027025）
Opened online:25 September 2008
Accepted by: none
Citation: Yanping Chen,Yong Ding,Dashan Fan.A Parabolic Singular Integral Operator With Rough Kernel[OL]. [25 September 2008] http://en.paper.edu.cn/en_releasepaper/content/24364
 
 
Let $Omega$ be an $H^1(S^{n-1})$ function on the unit sphere satisfying a certain cancellation condition. We study the $L^p$ boundedness of the singular integral operator $$T f(x)=hbox{p.v.}int_{{\\Bbb R}^n}f(x-y)Omega(y^prime)rho(y)^{-alpha},dy,$$ where $alphageq n$ and $rho$ is a norm function which is homogeneous with respect to certain nonistropic dilation. The result in the paper substantially improves and extends some known results.
Keywords:Parabolic singular integral;Hardy space;rough kernel
 
 
 

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