Authors: Li, Songxiao
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On an integral-type operator from iterated logarithmic Bloch spaces into Bloch-type spaces
Journal: Applied Mathematics and Computation
Volume: 215
Issue: 8
First page: 3106
Last page: 3115
Issue Date: 15-Dec-2009
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2009.10.004
Let H (B) denote the space of all holomorphic functions on the open unit ball B of Cn. Let φ = (φ1, ..., φn) be a holomorphic self-map of B and g ∈ H (B) such that g (0) = 0. In this paper we study the boundedness and compactness of the following integral-type operator, recently introduced by Xiangling Zhu and the second authorIφg f (z) = ∫01 R f (φ (tz)) g (tz) frac(dt, t), z ∈ B,from the iterated logarithmic Bloch spaces into the Bloch-type spaces. For the case when φ (z) ≡ z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic Bloch space into the little Bloch-type space.
Keywords: Bloch-type space | Boundedness | Compactness | Integral-type operator | Iterated logarithmic Bloch space
Publisher: Elsevier
Project: Educational Commission of Guangdong Province, China (No. LYM08092)

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