Integral-type operators acting between weighted-type spaces on the unit ball

Abstract

Let B denote the unit ball in Cn and H (B) the space of all holomorphic functions on B. We study the boundedness and compactness of the following integral-type operatorsIφg f (z) = ∫01 R f (φ (tz)) g (tz) frac(dt, t), z ∈ B,where g ∈ H (B), g (0) = 0, φ is a holomorphic self-map of B and R f is the radial derivative of f, between weighted-type spaces on the unit ball.