An integral type operator on Sᵖ spaces and its essential norm

Abstract

Given two analytic functions λ : D → D and ν : D → C and n ∈ N0, we study boundedness of the integral-type operator Cⁿλ,ν acting from derivative Hardy space into Zygmund space. We also get an approximation for the essential norm of this operator. A characterization for compactness of the operator can be obtained from the essential norm.