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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on the area theorem in the theory of univalent functions


Authors: M. Pavlović and José Ángel Peláez
Journal: Proc. Amer. Math. Soc. 139 (2011), 909-916
MSC (2010): Primary 30C55, 30H10
Published electronically: October 22, 2010
MathSciNet review: 2745643
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Abstract: We prove an integral extension of the classical area theorem for univalent functions. We give an application finding geometric conditions on the image domain of a univalent function $ f$ which imply that $ f$ belongs to the Hardy space $ H^p$, $ 0<p<\infty$.


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Additional Information

M. Pavlović
Affiliation: Miroslav Pavlović, Matematički fakultet, Studentski trg 16, 11001 Belgrade, p.p. 550, Serbia
Email: pavlovic@matf.bg.ac.yu

José Ángel Peláez
Affiliation: Departamento de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain
Email: japelaez@uma.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10333-7
PII: S 0002-9939(2010)10333-7
Keywords: Area theorem, univalent functions, Hardy spaces.
Received by editor(s): October 5, 2009
Received by editor(s) in revised form: December 15, 2009
Published electronically: October 22, 2010
Additional Notes: The first author is supported by MNZŽS Serbia, Project ON144010.
The second author is partially supported by the Ramón y Cajal program of MICINN (Spain), the Spanish (Grants MTM2007-60854 and MTM2006-26627) and regional Andalusian (Grants FQM210 and P06-FQM01504) governments.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society