On an integral-type operator between bloch-type spaces

Let H(B)H(B) denote the space of all holomorphic functions on the unit ball B   of CnCn. Let φφ be a holomorphic self-map of B   and g∈H(B)g∈H(B), such that g(0)=0.g(0)=0. We study the boundedness and compactness of the following integral-type operator recently introduced by StevićPφg(f)(z)=∫01f(φ(tz))g(tz)dtt,z∈B,between Bloch-type spaces. Our main results are natural extensions of some results in the following paper: S. Stević, On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball, J. Math. Anal. Appl. 354 (2009) 426–434.