Güngör, Nihan; Sağır, Birsen

Petranuarat and Kemprasit (Southeast Asian Bull Math 21:139–147, 1997) characterized continuity of the superposition operator acting from the sequence space lp into lq where 1 ≤ p, q < ∞. Sağır and Güngör defined the superposition operator Pg by Pg(x) = (g(k, s, xks))∞k,s=1 for all real double sequences (xks) where g: N2 × R → R and gave continuity of the superposition operator acting from the double sequence spaces Lp into Lq for 1 ≤ p, q < ∞. In this paper, we characterize the continuity of the superposition operator acting from Maddox double sequence spaces L(p) into L(q)where p = (pks) and q = (qks) are bounded double sequences of positive numbers.

Sağır, Birsen; Güngör, Nihan

In this paper, we define the superposition operator Pg where 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 → lq where 1 ≤ p; q < ∞, respectively. The main goal of this paper is to construct the necessary and sucient conditions for the continuity of Pg : Lp → L1 and Pg : Lp → Lq where 1 _ p; q < ∞.