The product-type operators from logarithmic Bloch spaces to Zygmund-type spaces

Abstract

The boundedness and compactness of a product-type operator, recently introduced by S. Stević, A. Sharma and R. Krishan, T n ψ 1 ,ψ 2 ,ϕ f (z) = ψ 1 (z) f (n) (ϕ(z)) + ψ 2 (z) f (n+1) (ϕ(z)), f ∈ H(D), from the logarithmic Bloch spaces to Zygmund-type spaces are characterized, where ψ 1 , ψ 2 ∈ H(D), ϕ is an analytic self-map of D and n a positive integer.