Continuity of superposition operators on the double sequence spaces of maddox L(p)

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.