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INTEGRABILITY OF THE DERIVATIVE OF A BLASCHKE PRODUCT

Published online by Cambridge University Press:  08 January 2008

Daniel Girela ,
José Ángel Peláez  and
Dragan Vukotić
Daniel Girela
Affiliation:
Departamento de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain (girela@uma.es)
José Ángel Peláez
Affiliation:
Departamento de Análisis Matemático, Universidad de Sevilla, Avenida de la Reina Mercedes, Apartado de correos 1160, 41080 Sevilla, Spain (japelaez@us.es)
Dragan Vukotić
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain (dragan.vukotic@uam.es)
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Abstract

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We study the membership of derivatives of Blaschke products in Hardy and Bergman spaces, especially for the the interpolating Blaschke products and for those whose zeros lie in a Stolz domain. We obtain new and very simple proofs of some known results and prove new theorems that complement or extend the earlier works of Ahern, Clark, Cohn, Kim, Newman, Protas, Rudin, Vinogradov and others.

Keywords

Primary 30D5030D5532A36Blaschke productsHardy spacesBergman spaces$Q_p$ spacesStolz angleinterpolating sequences
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 673 - 687
Copyright
Copyright © Edinburgh Mathematical Society 2007