Boundedness of superposition operators on the sequence spaces (w_0)_p(Phi)

Abstract

For a solid sequence space λ and a sequence of modulus functions Φ=(φ_k), let λ(Φ) = {x=(x_k) : Φ(x)=(φ_k(|x_k|))∈λ} . Provided another sequence of moduli Ψ = (ψ_k), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators from (w₀)_p(Φ) into l_q(Ψ) in the case 1≤p,q<∞.