Boundedness of superposition operators on the sequence spaces (w_0)_p(Phi)
Keywords:
sequence space, superposition operator, modulus function, boundedness
Abstract
For a solid sequence space λ and a sequence of modulus functions Φ=(φk), let λ(Φ) = {x=(xk) : Φ(x)=(φk(|xk|))∈λ} . Provided another sequence of moduli Ψ = (ψk), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators from (w0)p(Φ) into lq(Ψ) in the case 1≤p,q<∞.
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