Applications of Variants of the Hölder Inequality and its Inverses: Extensions of Barnes, Marshall-Olkin, and Nehari Inequalities.

Abstract

The primary aim of this paper is to extend Barnes [1], Marshall-Olkin [6], and Nehari [8] inequalities as applications of some results introduced in [10] by the author.Since several results from various sources are adopted here, a unified notation is required in order to simplify our subsequent arguments. To this end, let Lp = Lp(S, ∑, μ), p>0 (unless otherwise stated), be the space of all pth power non-negative integrable functions over a given finite measure space (S, ∑, μ) (where S may be regarded as a bounded subset of real numbers).