| |
|
|
| |
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: |
26D15.
|
|
| |
|
Editors: |
Bohumir Opic, |
|
| |
|
|
|
|
|
| |
|
Abstract: |
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.
|
|
|
|
|
|
| |
|
|
|
|
| |
|
|
|
|
|
Home
