Some Elementary Inequalities

Bennett, Grahame

doi:10.1093/qmath/38.4.401

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Introduction3

Proposition 4 Let1

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1995

2022

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Cited by 140 publications

(94 citation statements)

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“…Among the many papers that have appeared providing new proofs, generalizations and sharpenings of (1.1), we refer the reader to the work of G. Bennett [2]- [6] for his study of factorable matrices.…”

Section: Introductionmentioning

confidence: 99%

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A note on Hardy-type inequalities

Gao

2005

Proc. Amer. Math. Soc.

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Section: Introductionmentioning

confidence: 99%

“…However, we find that the following unpublished result of J. Cartlidge [8] is very useful to treat the above two inequalities. Here we quote his theorem according to [2] (Theorem C, p. 416):…”

Section: Introductionmentioning

confidence: 99%

A note on Hardy-type inequalities

Gao

2005

Proc. Amer. Math. Soc.

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“…We split the proof into two cases: α < and α = . For the case α < , Cα does not even map l p to l p , see [1,Corollary 8]. For the case α = , from Corollary 7 C is not p-summing.…”

Section: Proposition 4 Letmentioning

confidence: 99%

Absolutely Summing Terraced Matrices

Almasri

2016

Concrete Operators

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Let α > . By Cα we mean the terraced matrix de ned by c nk = n α if ≤ k ≤ n and if k > n. In this paper, we show that a necessary and su cient condition for the induced operator on l p , to be p-summing, is α > ; ≤ p < ∞. When the more general terraced matrix B, de ned by b nk = βn if ≤ k ≤ n and if k > n, is considered, the necessary and su cient condition turns out to be n n q p * | βn | q < ∞ in the region /p + /q ≤ .

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“…The main purpose of the present note is to establish two new Opial type inequalities involving partial sums. Our results are based on the Hardy inequality involving partial sums (see [2]- [4]) and the discrete analogue of the Opial inequality given by Wong in [10].…”

Section: Introductionmentioning

confidence: 99%