SCALING INVARIANT HARDY TYPE INEQUALITIES WITH NON-STANDARD REMAINDER TERMS

摘要

We consider the Hardy inequality on RN, the critical Hardy inequality on a ball, and the Rellich inequality on RN. These three Hardy type inequalities can be refined by adding remainder terms. Our remainder terms are expressed by a distance from the families of "virtual" extremals. A key ingredient is the critical Hardy inequality on RN which was proved by Machihara, Ozawa and Wadade [21].