Journal of Inequalities and Applications
Volume 2005 (2005), Issue 1, Pages 81-88
doi:10.1155/JIA.2005.81
Abstract
Let H(B) denote the space of all holomorphic functions on the unit ball B⊂ℂn. In this paper, we investigate the integral operator Tg(f)(z)=∫01f(tz)ℜg(tz)(dt/t), f∈H(B), z∈B, where g∈H(B) and ℜg(z)=∑j=1nzj(∂g/∂zj)(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.