On weighted hardy and Poincaré-type inequalities for differences

Abstract

A criterion is obtained for the Hardy-type inequality to be valid for and . This weakens a criterion previously found by the first two authors and comes close to being necessary as well as sufficient. When an inequality in the criterion is reversed, a Poincaré-type inequality is derived in some cases.

Keywords

• Hardy
• Poincaré
• inequalities
• differences