Continuity of Superposition Operators on the Double Sequence Spaces L

Continuity of Superposition Operators on the Double Sequence Spaces L

In this paper, we define the superposition operator Pgwhere g : N2 × R → R by Pg((xks)) = g (k,s,xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized Pg: lp→ l1 and Pg: lp→ lqwhere 1 ≤ p,q < ∞, respectively. The main goal of this paper...

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Veröffentlicht in:Filomat 2015-01, Vol.29 (9), p.2107-2118
Hauptverfasser: Sağır, Birsen, Güngör, Nihan
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Mathematical sequences
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description In this paper, we define the superposition operator Pgwhere g : N2 × R → R by Pg((xks)) = g (k,s,xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized Pg: lp→ l1 and Pg: lp→ lqwhere 1 ≤ p,q < ∞, respectively. The main goal of this paper is to construct the necessary and sufficient conditions for the continuity of Pg: Lp→ L1 and Pg: Lp→ Lqwhere 1 ≤ p,q < ∞.
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title Continuity of Superposition Operators on the Double Sequence Spaces L
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