Integral-type operators from Bloch-type spaces to Zygmund-type spaces

Abstract

Let H (B) denote the space of all holomorphic functions on the unit ball B ⊂ Cn. This paper investigates the following integral-type operator with symbol g ∈ H (B)Tg (f) (z) = ∫01 f (tz) R g (tz) frac(dt, t), f ∈ H (B), z ∈ B,where R g (z) = ∑j = 1n zj frac(∂ g, ∂ zj) (z) is the radial derivative of g. The boundedness and compactness of the operator Tg from Bloch-type spaces to Zygmund-type spaces are studied.