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  Volume 4, Issue 3, Article 61
Some New Hardy Type Inequalities and their Limiting Inequalities

    Authors: Anna Wedestig,  
    Keywords: Inequalities, Weights, Hardy's inequality, Pólya-Knopp's inequality, Multidimensional inequalities, Sawyer's two-dimensional operator.  
    Date Received: 12/12/02  
    Date Accepted: 08/09/03  
    Subject Codes:


    Editors: Bohumir Opic,  

A new necessary and sufficient condition for the weighted Hardy inequality is proved for the case . The corresponding limiting Pólya-Knopp inequality is also proved for . Moreover, a corresponding limiting result in two dimensions is proved. This result may be regarded as an endpoint inequality of Sawyer's two-dimensional Hardy inequality. But here we need only one condition to characterize the inequality whereas in Sawyer's case three conditions are necessary.

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