Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: RIEMANN-STIELTJES OPERATORS FROM F(p, q,s) SPACES TO α-BLOCH SPACES ON THE UNIT BALL | RIEMANN-STIELTJES OPERATORS FROM F p q s SPACES TO a-BLOCH SPaCeS on the unit ball SONGXIAO LI Received 5 December 2005 Accepted 19 April 2006 Let H B denote the space of all holomorphic functions on the unit ball B G Cn. We investigate the following integral operators Tg f z J01 f tz ivg tz dt t Lg f z J04l f tz g tz dt t ft H B z G B where ge H B an Ah z j Zj dh dzj z is the radial derivative of h. The operator Tg can be considered as an extension of the Cesaro 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 a-Bloch space a in the unit ball is discussed in this paper. 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. 1. Introduction Let z z1 . zn and w w1 . wn be points in the complex vector space Cn and z w 21W1 --- znwn. Let dv stand for the normalized Lebesgue measure on Cn. For a holomorphic function f we denote Vf dLf Ỵ f dzi . dzj Let H B denote the class of all holomorphic functions on the unit ball. Let it f z Xj i zj df dzj z stand for the radial derivative of f G H B 21 . It is easy to see that if f G H B f z yaaaza where a is a multiindex then ivf z a ữaza. Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2006 Article ID 27874 Pages 1-14 DOI JIA 2006 27874 2 Riemann-Stieltjes operators from F p q s to The a-Bloch space a B a a 0 is the space of all f G H B such that ba f sup 1- z 2F F l z I 00. zeB On the norm is introduced by Ilf 11 f 0 1 ba f . With this norm a is a Banach space. If a 1 we denote a simply by . For a z a 0 let tya denote the Mobius transformation of B taking 0 to a defined by a- Pa z - V1- z 2 Qa z tya z -----------7 7--------- 1 - z
