Authors: Avetisyan, Karen
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Extended Cesàro operators between different Hardy spaces
Journal: Applied Mathematics and Computation
Volume: 207
Issue: 2
First page: 346
Last page: 350
Issue Date: 15-Jan-2009
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2008.10.055
Let Hp denote the Hardy space of holomorphic functions on the unit ball B. This note gives some sufficient and necessary conditions for the boundedness and compactness of the following extended Cesàro 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),where z ∈ B and g is a fixed holomorphic map on B, acting from the space Hp into the space Hq, for the case p < q. Our results extend and simplify some one-dimensional results.
Keywords: Bloch space | Boundedness | Compactness | Extended Cesàro operators | Hardy space | Unit ball
Publisher: Elsevier

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