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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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Convex harmonic mappings are not necessarily in $h^{1/2}$
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by Alexandru Aleman and María J. Martín PDF
Proc. Amer. Math. Soc. 143 (2015), 755-763 Request permission

Abstract:

We construct convex harmonic mappings in the unit disk that do not belong to the harmonic Hardy space $h^{1/2}$. This provides a negative answer to a question raised by P. Duren.
References
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Additional Information
  • Alexandru Aleman
  • Affiliation: Department of Mathematics, Lund University, P. O. Box 118, S-221 00 Lund, Sweden
  • Email: aleman@maths.lth.se
  • María J. Martín
  • Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
  • Email: maria.martin@uef.fi
  • Received by editor(s): March 4, 2013
  • Received by editor(s) in revised form: May 21, 2013
  • Published electronically: October 10, 2014
  • Additional Notes: This work was supported by Grant MTM2012-37436-C02-02, MINECO, Spain. The second author was also partially supported by “Beca Fundación Caja Madrid. Movilidad de Profesores, Convocatoria 2012/13”, Spain
  • 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), 755-763
  • MSC (2010): Primary 30C45; Secondary 30H10, 31A05
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12281-7
  • MathSciNet review: 3283662