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  Volume 4, Issue 4, Article 81
 
Weighted Weak Type Inequalities For The Hardy Operator When $p = 1$

    Authors: Tieling Chen,  
    Keywords: Hardy operator, Weak type inequality.  
    Date Received: 23/06/03  
    Date Accepted: 22/09/03  
    Subject Codes:

26D15.

  
    Editors: Terry M. Mills,  
 
    Abstract:

The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted $ L^p$ to weighted weak $ L^q$ in the case $ p = 1$. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when $ p = 1$. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when $ qp=1$. The best constant in the inequality is also estimated.

         
       
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