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  • Research Article
  • Open Access

Weighted inequalities for the Sawyer two-dimensional Hardy operator and its limiting geometric mean operator

Journal of Inequalities and Applications20052005:374053

  • Received: 3 November 2003
  • Published:


We consider and a corresponding geometric mean operator . E. T. Sawyer showed that the Hardy-type inequality could be characterized by three independent conditions on the weights. We give a simple proof of the fact that if the weight is of product type, then in fact only one condition is needed. Moreover, by using this information and by performing a limiting procedure we can derive a weight characterization of the corresponding two-dimensional Pólya-Knopp inequality with the geometric mean operator involved.

Authors’ Affiliations

Department of Mathematics, Luleå University, Luleå, 97 187, Sweden


© Wedestig. 2005