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  Volume 8, Issue 1, Article 26
 
On the Iterated Green Functions on a Bounded Domain and Their Related Kato Class of Potentials

    Authors: Habib M‚agli, Noureddine Zeddini,  
    Keywords: Green function, Gauss semigroup, Kato class.  
    Date Received: 30/05/06  
    Date Accepted: 18/02/07  
    Subject Codes:

34B27.

 
    Editors: Neil S. Barnett,  
 
    Abstract:

We use the results of Zhang [15,16] and Davies [7] on the behavior of the heat kernel $ p(t,x,y)$ on a bounded $ C^{1,1}$ domain $ D$ to find again the result of Grunau-Sweers [9] concerning the estimates of the iterated Greens functions $ G_{m,n}(D)$. Next, we use these estimates to characterize, by means of $ p(t,x,y)$, the Kato class $ K_{m,n}(D)$ and we give new examples of functions belonging to this class.

         
       
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