An Integral-Type Operator from H^∞ to Zygmund-Type Spaces

Let g∈H(D), n be a nonnegative integer and φ be an analytic self-map of D. We study the boundedness and compactness of the integral operator C n φ,g defined by (C n φ,g f)(z)=∫z 0 f^(n)(φ(ξ))g(ξ)dξ,z∈D, f∈H(D), from H^∞ to Zygmund-type spaces on the unit disk.