On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball

摘要

Let𝔹denote the open unit ball ofℂn. For a holomorphic self-mapφof𝔹and a holomorphic functiongin𝔹withg(0)=0, we define the following integral-type operator:Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t),z∈𝔹. Hereℜfdenotes the radial derivative of a holomorphic functionfin𝔹. We study the boundedness and compactness of the operator between Bloch-type spacesℬωandℬμ, whereωis a normal weight function andμis a weight function. Also we consider the operator between the little Bloch-type spacesℬω,0andℬμ,0.