Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 789285, 14 pages
doi:10.1155/2010/789285
Research Article

Integral-Type Operators from 𝐹 ( 𝑝 , 𝑞 , 𝑠 ) Spaces to Zygmund-Type Spaces on the Unit Ball

Congli Yang1,2

1Department of Mathematics and Computer Science, Guizhou Normal University, 550001 Gui Yang, China
2Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland

Received 7 May 2010; Revised 21 September 2010; Accepted 23 December 2010

Academic Editor: Siegfried Carl

Copyright © 2010 Congli Yang. 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 ⊂ ℂ 𝑛 . This paper investigates the following integral-type operator with symbol g ∈ 𝐻 ( 𝔹 ) , 𝑇 g ∫ 𝑓 ( 𝑧 ) = 1 0 𝑓 ( 𝑡 𝑧 ) ℜ g ( 𝑡 𝑧 ) 𝑑 𝑡 / 𝑡 , 𝑓 ∈ 𝐻 ( 𝔹 ) , 𝑧 ∈ 𝔹 , where ℜ g ∑ ( 𝑧 ) = 𝑛 𝑗 = 1 𝑧 𝑗 𝜕 g / 𝜕 𝑧 𝑗 ( 𝑧 ) is the radial derivative of g . We characterize the boundedness and compactness of the integral-type operators 𝑇 g from general function spaces 𝐹 ( 𝑝 , 𝑞 , 𝑠 ) to Zygmund-type spaces 𝒵 𝜇 , where 𝜇 is normal function on [ 0 , 1 ) .