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Inner functions with derivatives in the weak Hardy space


Authors: Joseph A. Cima and Artur Nicolau
Journal: Proc. Amer. Math. Soc. 143 (2015), 581-594
MSC (2010): Primary 30H05, 30H10
DOI: https://doi.org/10.1090/S0002-9939-2014-12305-7
Published electronically: October 1, 2014
MathSciNet review: 3283646
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Abstract: It is proved that exponential Blaschke products are the inner functions whose derivative is in the weak Hardy space. As a consequence, it is shown that exponential Blaschke products are Frostman shift invariant. Exponential Blaschke products are described in terms of their logarithmic means and also in terms of the behavior of the derivatives of functions in the corresponding model space.


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Additional Information

Joseph A. Cima
Affiliation: Department of Mathematics, University of North Carolina, 305 Phillips Hall, Chapel Hill, North Carolina 27599-3250

Artur Nicolau
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

DOI: https://doi.org/10.1090/S0002-9939-2014-12305-7
Received by editor(s): February 6, 2013
Published electronically: October 1, 2014
Additional Notes: The second author was supported in part by the grants MTM2011-24606 and 2009SGR420
It is a pleasure for the authors to thank the referee for a careful reading of the paper
Communicated by: Pamela B. Gorkin
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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