|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||Abstract:||
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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