Authors: Stević, Stevo 
Sharma, Ajay
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Composition operators from the space of Cauchy transforms to Bloch and the little Bloch-type spaces on the unit disk
Journal: Applied Mathematics and Computation
Volume: 217
Issue: 24
First page: 10187
Last page: 10194
Issue Date: 15-Aug-2011
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2011.05.014
Abstract: 
We completely characterize the boundedness and compactness of composition operators from the space of Cauchy transforms on the unit disk D, into the Bloch-type space Bν as well as the little Bloch-type space Bν,0, consisting respectively of all holomorphic functions f on D such that supz∈Dν(z)|f′(z)|<∞, that is, of all holomorphic functions f on D such that lim|z|→1ν (z)|f′(z)|=0, for some weight function ν. As a byproduct of our results, norm of the operator is calculated when Bν is replaced by Bν/C.
Keywords: Bloch-type space | Boundedness | Cauchy transform | Compactness | Composition operator
Publisher: Elsevier
Project: Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
National Board of Higher Mathematics, India (Grant No. 48/4/2009/R&D-II/426)

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