An index of summability for pairs of Banach spaces

Maia, Mariana; Pellegrino, Daniel; Santos, Joedson

doi:10.1016/j.jmaa.2016.04.030

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Cited by 2 publications

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“…This paper is a natural continuation of [2] and, in some sense it is also related to the notion of index of summability introduced by Maia, Pellegrino and Santos [11], which essentially investigates what dependence on n emerges when we perturb some well known inequalities (for instance in (1.1)).…”

Section: Introductionmentioning

confidence: 99%

Summability of multilinear forms on classical sequence spaces

Nogueira

Rueda

2017

Quaestiones Mathematicae

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We present an extension of the Hardy-Littlewood inequality for multilinear forms. More precisely, let K be the real or complex scalar field and m, k be positive integers with m ≥ k and n 1 , . . . , n k be positive integers such that n 1 + · · · + n k = m.T for all m-linear forms T : ℓ n p × · · · × ℓ n p → K and all positive integers n. Moreover, the exponent max 2kp−kpr−pr+2rm 2pr , 0 is optimal.T for all m-linear forms T : ℓ n p × · · · × ℓ n p → K and all positive integers n. Moreover, the exponent max p−rp+rm pr , 0 is optimal. The case k = m recovers a recent result due to G. Araujo and D. Pellegrino.

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Section: Introductionmentioning

confidence: 99%