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

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

Blog Article

We consider and a corresponding hand pulse set 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 Shampoo 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.