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

Abstract EN

Let ? denote the open unit ball of ℂn.

For a holomorphic self-map φ of ? and a holomorphic function g in ? with g(0)=0, we define the following integral-type operator: Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t), z∈?.

Here ℜf denotes the radial derivative of a holomorphic function f in ?.

We study the boundedness and compactness of the operator between Bloch-type spaces ℬω and ℬμ, where ω is a normal weight function and μ is a weight function.

Also we consider the operator between the little Bloch-type spaces ℬω,0 and ℬμ,0.