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Transactions of the American Mathematical Society

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On Riesz type inequalities for harmonic mappings on the unit disk


Author: David Kalaj
Journal: Trans. Amer. Math. Soc. 372 (2019), 4031-4051
MSC (2010): Primary 47B35
DOI: https://doi.org/10.1090/tran/7808
Published electronically: March 26, 2019
MathSciNet review: 4009386
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Abstract: We prove some sharp inequalities for complex harmonic functions on the unit disk. The results extend a M. Riesz conjugate function theorem and some well-known estimates for holomorphic functions. We apply some of results to the isoperimetric inequality for harmonic mappings.


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Additional Information

David Kalaj
Affiliation: Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put b.b. 81000 Podgorica, Montenegro
Email: davidk@ac.me

DOI: https://doi.org/10.1090/tran/7808
Keywords: Subharmonic functions, harmonic mappings
Received by editor(s): December 17, 2017
Received by editor(s) in revised form: July 19, 2018
Published electronically: March 26, 2019
Article copyright: © Copyright 2019 American Mathematical Society