Journal of Inequalities and Applications
Volume 2005 (2005), Issue 1, Pages 81-88

On an integral operator on the unit ball in n

Stevo Stević

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.


Let H(B) denote the space of all holomorphic functions on the unit ball Bn. In this paper, we investigate the integral operator Tg(f)(z)=01f(tz)g(tz)(dt/t), fH(B), zB, where gH(B) and g(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.