Authors: Li, Songxiao
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Cesàro-type operators on some spaces of analytic functions on the unit ball
Journal: Applied Mathematics and Computation
Volume: 208
Issue: 2
First page: 378
Last page: 388
Issue Date: 15-Feb-2009
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2008.12.006
Let H (B) denote the space of all holomorphic functions on the unit ball B ⊂ Cn. In this paper we investigate the following integral operators:Tg (f) (z) = ∫01 f (tz) R g (tz) frac(dt, t) and Lg (f) (z) = ∫01 R f (tz) g (tz) frac(dt, t),where f ∈ H (B), z ∈ B, g ∈ H (B) and R h (z) = ∑j = 1n zj frac(∂ 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 and compactness of the operators Tg and Lg, on the Zygmund space and from the Zygmund space to the Bloch space are studied.
Keywords: Bloch space | Boundedness | Compactness | Extended Cesàro operator | Unit ball | Zygmund space
Publisher: Elsevier
Project: NSF of Guangdong Province (No. 7300614)

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