A collection of inequalities based on the Carleman integral inequality

Year 2025, Volume: 1 Issue: 1, 1 - 10, 28.11.2025

Christophe Chesneau

Abstract

This article presents a collection of new inequalities derived from the Carleman integral inequality. Several of these results incorporate auxiliary elements, such as secondary, reciprocal and primitive functions, as well as Laplace transforms. Complete proofs are provided, making use of a variety of well-established inequalities and analytical techniques. Many of these methods are broadly applicable and can be adapted to other contexts involving integral inequalities.

Keywords

Carleman integral inequality , Laplace transform , reciprocal function , Young product inequality , Chebyshev integral inequality , Hölder integral inequality

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