Remarks on the area theorem in the theory of univalent functions
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- by M. Pavlović and José Ángel Peláez PDF
- Proc. Amer. Math. Soc. 139 (2011), 909-916 Request permission
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 $H^p$, $0<p<\infty$.References
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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
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 909-916
- MSC (2010): Primary 30C55, 30H10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10333-7
- MathSciNet review: 2745643