Regularity of the coefficients of multilinear forms on sequence spaces

Pellegrino, Daniel; Raposo, Anselmo

doi:10.48550/arxiv.2112.12829

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2022

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“…The investigation of extensions of the Hardy-Littlewood inequalities to multilinear forms were initiated by Praciano-Pereira [8] in 1981 and intensively investigated since then (see, for instance, [9][10][11][12][13]7,14,15]), but there are still several open problems regarding the optimal exponents and optimal constants involved. Daniel M. Pellegrino, Anselmo Raposo Jr., and Diana M. Serrano-Rodríguez [16] explore a regularity technique to obtain optimal parameters for several results in this frame work extending generalizing theorem of Paulino [14] and others.…”

Section: Introductionmentioning

confidence: 99%

The Orlicz Inequality for Series of Multilinear Forms

Salih

Hussein

2022

JAMCS

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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 ≤ ∞.

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