Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Integral-type operators between α-Bloch spaces and Besov spaces on the unit ball
Journal: Applied Mathematics and Computation
Volume: 216
Issue: 12
First page: 3541
Last page: 3549
Issue Date: 15-Aug-2010
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2010.04.074
Let H (B) denote the space of all holomorphic functions on the unit ball B ⊂ Cn. The boundedness and compactness of the following integral-type operatorsTg (f) (z) = ∫01 f (tz) R g (tz) frac(dt, t) and Lg (f) (z) = ∫01 R f (tz) g (tz) frac(dt, t), z ∈ B,where g ∈ H (B) and R h (z) is the radial derivative of h, between α-Bloch spaces and Besov spaces on the unit ball are characterized. The results regarding the case when these operators map α-Bloch spaces to Besov spaces are nontrivial generalizations of recent one-dimensional results by Li and the present author.
Keywords: α-Bloch space | Besov space | Boundedness | Compactness | Integral-type operator | Unit ball
Publisher: Elsevier

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