Abstract and Applied Analysis
Volume 2010 (2010), Article ID 214762, 14 pages
doi:10.1155/2010/214762
Research Article

On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball

Stevo Stević1 and Sei-Ichiro Ueki2

1Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia
2Faculty of Engineering, Ibaraki University, Hitachi 316-8511, Japan

Received 30 January 2010; Accepted 18 March 2010

Academic Editor: Narcisa C. Apreutesei

Copyright © 2010 Stevo Stević and Sei-Ichiro Ueki. 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 𝔹 denote the open unit ball of ℂn. For a holomorphic self-map φ of 𝔹 and a holomorphic function g in 𝔹 with g(0)=0, we define the following integral-type operator: Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t), z∈𝔹. Here ℜf denotes the radial derivative of a holomorphic function f in 𝔹. We study the boundedness and compactness of the operator between Bloch-type spaces ℬω and ℬμ, where ω is a normal weight function and μ is a weight function. Also we consider the operator between the little Bloch-type spaces ℬω,0 and ℬμ,0.