JIPAM

Norms of Certain Operators on Weighted $\ell_p$Spaces and Lorentz Sequence Spaces  
 
  Authors: Graham Jameson, R. Lashkaripour,  
  Keywords: Hardy's inequality, Hilbert's inequality, Norms of operators.  
  Date Received: 07/05/01  
  Date Accepted: 21/09/01  
  Subject Codes:

26D15,15A60,47B37.

  
  Editors: Bohumir Opic,  
 
  Abstract:

The problem addressed is the exact determination of the norms of the classical Hilbert, Copson and averaging operators on weighted $ell_p$ spaces and the corresponding Lorentz sequence spaces $d(w,p)$, with the power weighting sequence $w_n = n^{-alpha }$ or the variant defined by $w_1+ cdots +w_n = n^{1-alpha }$. Exact values are found in each case except for the averaging operator with $w_n = n^{-alpha }$, for which estimates deriving from various different methods are obtained and compared.;


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