## 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