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  Volume 4, Issue 3, Article 53
 
Carleman's Inequality - History, Proofs and Some New Generalizations

    Authors: Maria Johansson, Lars-Erik Persson, Anna Wedestig,  
    Keywords: Inequalities, Carleman's inequality, Pólya-Knopp's inequality, Sharp constants, Proofs, Weights, Historical remarks.  
    Date Received: 04/12/02  
    Date Accepted: 25/03/03  
    Subject Codes:

26D15

 
    Editors: Saburou Saitoh,  
 
    Abstract:

Carleman's inequality reads

   

where , are positive numbers. In this paper we present some simple proofs of and several remarks (e.g. historical) about the inequality and its corresponding continuous version. Moreover, we discuss and comment on some very new results. We also include some new proofs and results e.g. a weight characterization of a general weighted Carleman type inequality for the case 0 p q We also include some facts about T. Carleman and his work.

         
       
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