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On the $L^1$ Norm of the Weighted Maximal Function of Fejér Kernels with Respect to the Walsh-Kaczmarz System  
 
  Authors: Károly Nagy,  
  Keywords: Walsh-Kaczmarz system, Fejér kernels, Fejér means, Maximal operator.  
  Date Received: 24/05/2007  
  Date Accepted: 15/02/2008  
  Subject Codes:

42C10.

  
  Editors: Zsolt Pales,  
 
  Abstract:

The main aim of this paper is to investigate the integral of the weighted maximal function of the Walsh-Kaczmarz-Fejér kernels. We give a necessary and sufficient conditions for that the weighted maximal function of the Walsh-Kaczmarz-Fejér kernels is in $ L^1$. After this we discuss the weighted maximal function of $ (C,alpha)$ kernels with respect to Walsh-Paley system too. ;


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