New Hardy-Type Inequalities Via Opial Inequalities

TL;DR

This paper introduces new Hardy-type inequalities with explicit constants, derived using generalized Opial and Hölder inequalities, and explores their applications to differential inequalities of Wirtinger type.

Contribution

It presents a novel method employing generalized Opial inequalities to establish Hardy-type inequalities with explicit constants.

Findings

New Hardy-type inequalities with explicit constants

Application to differential inequalities of Wirtinger type

Introduction of a novel proof technique using Opial inequalities

Abstract

In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older'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 typ