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Estimates for the Green function and Characterization of a Certain Kato Class by the Gauss Semigroup in the Half Space  
 
  Authors: Imed Bachar,  
  Keywords: Green functions, $3G$-theorem, Kato class.  
  Date Received: 06/07/05  
  Date Accepted: 11/08/05  
  Subject Codes:

34B27.

  
  Editors: Catherine Bandle,  
 
  Abstract:

We establish a $ 3G$-theorem for the Green functions $ G_{m,n}$ of $ (-Delta )^{m}$ $ (mgeq 1)$ on $ mathbb{R}_{+}^{n}:={x=(x_{1},dots,x_{n})in mathbb{R }^{n}:x_{n}>0},$ $ ngeq 2m-1,$ with Navier boundary conditions $ Delta ^{j}umid _{partial mathbb{R}_{+}^{n}}=0,$ $ 0leq jleq m-1$.

We exploit these results to define a certain Kato class of functions that we characterize by means of the Gauss semigroup on $ mathbb{R}_{+}^{n}.$;


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