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    STUDIA MATHEMATICA - Issue no. 1 / 2007  
         
  Article:   ON THE APPROXIMATION NUMBERS OF CERTAIN VOLTERRA INTEGRAL OPERATORS BETWEEN LEBESGUE SPACES.

Authors:  MOHAMED ACHACHE.
 
       
         
  Abstract:  

The aim of the paper is to study certain Volterra integral operators of the form

which defines linear maps between the Lebesgue spaces Lp(R ) and Lq(R ) where 1 < q < p < oo. Under some conditions of the integrability on its kernel, we show some important properties for T such as boundedness, compactness, the measureof non compactness and estimating, upper and lower bounds for its approximation numbers. These estimates have an application to the spectral properties of Sturm-Liouville differential operators.

 
         
     
         
         
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