Integral-type operators between α-Bloch spaces and Besov spaces on the unit ball

Abstract

Let H (B) denote the space of all holomorphic functions on the unit ball B ⊂ Cn. The boundedness and compactness of the following integral-type operatorsTg (f) (z) = ∫01 f (tz) R g (tz) frac(dt, t) and Lg (f) (z) = ∫01 R f (tz) g (tz) frac(dt, t), z ∈ B,where g ∈ H (B) and R h (z) is the radial derivative of h, between α-Bloch spaces and Besov spaces on the unit ball are characterized. The results regarding the case when these operators map α-Bloch spaces to Besov spaces are nontrivial generalizations of recent one-dimensional results by Li and the present author.