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Another approach to characterizations of generalized triangle inequalities in normed spaces

100%
Izumida T., Mitani K.-I., Saito K.-S.
Open Mathematics
|
2014
|
tom 12
|
nr 11
1615-1623
EN
In this paper, we consider a generalized triangle inequality of the following type: $$\left\| {x_1 + \cdots + x_n } \right\|^p \leqslant \frac{{\left\| {x_1 } \right\|^p }} {{\mu _1 }} + \cdots + \frac{{\left\| {x_2 } \right\|^p }} {{\mu _n }}\left( {for all x_1 , \ldots ,x_n \in X} \right),$$ where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].
2
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Weighted multilinearp-adic Hardy operators and commutators

76%
Liu R., Zhou J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1623-1634
EN
In this paper, the weighted multilinear p-adic Hardy operators are introduced, and their sharp bounds are obtained on the product of p-adic Lebesgue spaces, and the product of p-adic central Morrey spaces, the product of p-adic Morrey spaces, respectively. Moreover, we establish the boundedness of commutators of the weighted multilinear p-adic Hardy operators on the product of p-adic central Morrey spaces. However, it’s worth mentioning that these results are different from that on Euclidean spaces due to the special structure of the p-adic fields.
3
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Composition results for strongly summing and dominated multilinear operators

64%
Popa D.
Open Mathematics
|
2014
|
tom 12
|
nr 10
1433-1446
EN
In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.
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