Home > Papers

 
 
A note on a conjecture of Calder′on on weak type L1 boundedness of CZOs
Chen Jiecheng * #,Zhu Xiangrong
Department of Mathematics,Zhejiang University
*Correspondence author
#Submitted by
Subject:
Funding: 教育部博士点基金，Supported by 973 project (G1999075105), NSFZJ(RC97017), NSFC(10571156)（No.20030335019）
Opened online: 1 December 2006
Accepted by: none
Citation: Chen Jiecheng,Zhu Xiangrong.A note on a conjecture of Calder′on on weak type L1 boundedness of CZOs[OL]. [ 1 December 2006] http://en.paper.edu.cn/en_releasepaper/content/10111
 
 
For $f\\in \\QTR{cal}{S}(R^2)$ and $\\Omega \\in L^1(S^1)$, $\\int_{S^1}\\Omega (x^{\\prime })dx^{\\prime }=0$, define $$T_\\Omega (f)(x)=\\underset{\\epsilon \\rightarrow 0+}\\to{\\lim }\\int_{\\left| x-y\\right| \\geq \\epsilon }\\frac{\\Omega (y/\\left| y\\right| )}{\\left| y\\right| ^2}f(x-y)dy. $$In this paper, we shall prove that there are a class of functions in $H^1(S^1)-L\\ln {}^{+}L(S^1)$ such that $T_\\Omega $ is weak type $L^1-$bounded.
Keywords:Calder\\\
 
 
 

For this paper
  • ● PDF (0B)
  • ● Revision 0 　　
  • ● Print this paper
  • ● Recommend this paper to a friend
  • ● Add to my favorite list

    Saved Papers

    Please enter a name for this paper to be shown in your personalized Saved Papers list

Tags
Add yours

Related Papers

Statistics
PDF Downloaded 566
Bookmarked 0
Recommend 5
Comments Array
Submit your papers