On an integral operator on the unit ball in ℂn

Abstract

Let H(B) denote the space of all holomorphic functions on the unit ball B c ℂ n . In this paper, we investigate the integral operator T g (f)(z) = f 01 f (tz)ℜg(tz)(dt/t), f ∈ H(B), z ∈ B, where g ∈ H (B) and ℜg(z) = ∑ j=1n = Z j (∂g/∂z j )(z) is the radial derivative of g. The operator can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of the operator on a-Bloch spaces is considered.