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Convex harmonic mappings are not necessarily in $ h^{1/2}$


Authors: Alexandru Aleman and María J. Martín
Journal: Proc. Amer. Math. Soc. 143 (2015), 755-763
MSC (2010): Primary 30C45; Secondary 30H10, 31A05
Published electronically: October 10, 2014
MathSciNet review: 3283662
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2014-12281-7
Keywords: Convex harmonic mappings, Hardy spaces
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.