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  Volume 9, Issue 4, Article 110
 
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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