New Hardy-Type Inequalities Via Opial Inequalities

Abstract

In this paper, we will prove several new inequalities of Hardy's type with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and Hölder's inequality. To the best of the author's knowledge this method has not been used before in investigation of this type of inequalities. From these inequalities one can establish some new inequalities of differential forms which are inequalities of Wirtinger's type.