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Research Article Open access CC BY 4.0

The Orlicz Inequality for Series of Multilinear Forms

Salih Yousuf Mohamed Salih, Shawgy Hussein

Journal of Advances in Mathematics and Computer Science · pp. 52–66 · Published 22 Dec 2022

10.9734/jamcs/2022/v37i121728

Abstract

The Orlicz ( \(\ell\)2,\(\ell\)1)-mixed inequality of integers and fractional dimensions who states that, with a bit of extend, for all sequences of bilinear forms AL: \(\mathbb{K}\)n x \(\mathbb{K}\)n  \(\rightarrow\) \(\mathbb{K}\) and all positive integers n, where  \(\mathbb{K}\)n denotes  \(\mathbb{R}\)n or  \(\mathbb{C}\)n endowed with the supremum norm. For that we follow D.Núñez-Alarcón, D. Pellegrino, and D. Serrano-Rodríguez [1]] to extend this inequality to series of multilinear forms, with \(\mathbb{K}\)n endowed with \(\ell\)1+ \(\epsilon\) norms for all successive gradually of the general 0 ≤ ϵ ≤ ∞.

Orlicz inequality multilinear forms hölder inequality hardy-littlewood inequalities maurey-pisier factorization

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