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Two-dimensional Sunouchi Operator with respect to Vilenkin-like Systems  
 
  Authors: Chuanzhou Zhang, Xueying Zhang,  
  Keywords: Sunouchi operator, Vilenkin-like systems.  
  Date Received: 05/05/07  
  Date Accepted: 19/20/08  
  Subject Codes:

42C10.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

In this paper two-dimensional Vilenkin-like systems will be investigated. We prove the Sunouchi operator is bounded from $ H^q$ to $ L^q$ for $ (2/3<q\leq 1) $. As a consequence, we prove the Sunouchi operator is $ L^s$ bounded for $ 1<s<\infty$ and of weak type $ (H^\natural,L^1)$. ;


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