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 OBDII T-Harness is of product type, then in fact only one condition is needed.
Moreover, by using this information and by Shower Gel performing a limiting procedure we can derive a weight characterization of the corresponding two-dimensional Pólya-Knopp inequality with the geometric mean operator involved.