The continuity of superposition operators on some sequence spaces defined by moduli

Let lambda and mu be solid sequence spaces. For a sequence of modulus functions Phi = (phi(k)) let lambda(Phi) = {x = (x(k)): (phi(k)(vertical bar x(k)vertical bar)) is an element of lambda}. Given another sequence of modulus functions Psi = (Psi(k)), we characterize the continuity of the superposition operators P-f from lambda(Phi) into mu(Psi) for some Banach sequence spaces A and It under the assumptions that the moduli phi(k) (k is an element of N) are unbounded and the topologies on the sequence spaces lambda(Phi) and mu(Psi) are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type.