Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 27874, 14 pages
doi:10.1155/JIA/2006/27874

Riemann-Stieltjes operators from F(p,q,s) spaces to α-Bloch spaces on the unit ball

Songxiao Li1,2

1Department of Mathematics, JiaYing University, Meizhou 514015, GuangDong, China
2Department of Mathematics, Shantou University, Shantou 515063, GuangDong, China

Received 5 December 2005; Accepted 19 April 2006

Copyright © 2006 Songxiao Li. 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. We investigate the following integral operators: Tg(f)(z)=∫01f(tz)ℜg(tz)(dt/t), Lg(f)(z)=∫01ℜf(tz)g(tz)(dt/t), f∈H(B), z∈B, where g∈H(B), and ℜh(z)=∑j=1nzj(∂h/∂zj)(z) is the radial derivative of h. The operator Tg can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of two classes of Riemann-Stieltjes operators from general function space F(p,q,s), which includes Hardy space, Bergman space, Qp space, BMOA space, and Bloch space, to α-Bloch space ℬα in the unit ball is discussed in this paper.