JIPAM

On Certain Rough Integral Operators and Extrapolation  
 
  Authors: Hussain Al-Qassem, Leslie Cheng, Yibiao Pan,  
  Keywords: Maximal operator, Rough kernel, Singular integral, Orlicz spaces, Block spaces, Extrapolation, $L^p$ boundedness.  
  Date Received: 24/01/2009  
  Date Accepted: 31/08/2009  
  Subject Codes:

Primary 42B20; Secondary 42B15, 42B25.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

In this paper, we obtain sharp $ L^{p}$ estimates of two classes of maximal operators related to rough singular integrals and Marcinkiewicz integrals$ .$ These estimates will be used to obtain similar estimates for the related singular integrals and Marcinkiewicz integrals. By the virtue of these estimates and extrapolation we obtain the $ L^{p}$ boundedness of all the aforementioned operators under rather weak size conditions. Our results represent significant improvements as well as natural extensions of what was known previously. ;


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