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

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.