On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions

Year 2025, Volume: 13 Issue: 1, 87 - 92, 30.04.2025

Christophe Chesneau

Abstract

The focus of this article is a Hardy-type integral inequality published in 2012, which has the particularity of combining convexity and submultiplicativity assumptions. A revision is carried out in several steps. First, a counterexample to this result is given, questioning its validity. Then an alternative statement is proposed, together with a detailed proof. Among the facts revealed is the relaxation of the assumption on a key parameter of the integral norm. Finally, several examples of the revised result are presented, showing a new modification of the Hardy integral inequality. Their originality takes advantage of the combined convexity and submultiplicativity assumptions, which remain an underexplored framework.

Keywords

Hardy-type integral inequality, integral norms, submultiplicativity, convexity

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