Journal of Inequalities and Applications
Volume 2005 (2005), Issue 1, Pages 81-88
doi:10.1155/JIA.2005.81
On an integral operator on the unit ball in ℂn
Mathematical Institute of Serbian Academy of Sciences and Arts, Knez Mihailova 35/I, Beograd 11000, Serbia
Received 23 December 2003
Copyright © 2005 Stevo Stević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.