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Derivatives of Blaschke products whose zeros lie in a Stolz domain and weighted Bergman spaces


Author: Atte Reijonen
Journal: Proc. Amer. Math. Soc. 146 (2018), 1173-1180
MSC (2010): Primary 30J10; Secondary 30H20
DOI: https://doi.org/10.1090/proc/13791
Published electronically: October 6, 2017
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Abstract: For a Blaschke product $ B$ whose zeros lie in a Stolz domain, we find a condition regarding $ \omega $ which guarantees that $ B'$ belongs to the Bergman space $ A^p_\omega $. In addition, the sharpness of this condition is considered.


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Additional Information

Atte Reijonen
Affiliation: University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland
Email: atte.reijonen@uef.fi

DOI: https://doi.org/10.1090/proc/13791
Keywords: Bergman space, Blaschke product, doubling weight, inner function, Stolz domain
Received by editor(s): November 25, 2016
Received by editor(s) in revised form: April 25, 2017
Published electronically: October 6, 2017
Additional Notes: This research was supported in part by Academy of Finland project no. 268009, JSPS Postdoctoral Fellowship for North American and European Researchers, and North Karelia Regional Fund of Finnish Cultural Foundation.
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2017 American Mathematical Society

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