On an integral-type operator from the Bloch space to mixed norm spaces

Abstract

Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0)=0, where H(B) is the space of all holomorphic functions on the unit ball B of Cn. In this paper we investigate the following integral-type operatorDφgf(z)=∫01Df(φ(tz))g(tz)dtt,f∈H(B),where Df is the fractional derivative of f ∈ H(B). The boundedness and compactness of the operators Dφg between mixed norm spaces and Bloch spaces in the unit ball are studied.