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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inner functions with derivatives in the weak Hardy space
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by Joseph A. Cima and Artur Nicolau PDF
Proc. Amer. Math. Soc. 143 (2015), 581-594 Request permission

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
  • MR Author ID: 49485
  • Artur Nicolau
  • Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 3283646