On an integral-type operator acting between bloch-type spaces on the unit ball

Abstract

Let B denote the open unit ball ℂ of n. For a holomorphic self-map ∞ of B and a holomorphic function g in B with g(0) = 0, we define the following integral-type operator: I∞g f (z) = ∫01 ℛf(∞(tz))g(tz)(dt/t), z ∈ B Here ℛ f denotes the radial derivative of a holomorphic function f in B. 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 Bω0 and, Bμ0.