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

 

A Markov-type inequality for arbitrary plane continua


Author: Alexandre Eremenko
Journal: Proc. Amer. Math. Soc. 135 (2007), 1505-1510
MSC (2000): Primary 41A17, 26D05
Published electronically: November 29, 2006
MathSciNet review: 2276660
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Abstract | References | Similar Articles | Additional Information

Abstract: Markov's inequality is

$\displaystyle \sup_{[-1,1]}\vert f'\vert\leq(\deg f)^2\sup_{[-1,1]}\vert f\vert,$

for all polynomials $ f$. We prove a precise version of this inequality with an arbitrary continuum in the complex plane instead of the interval $ [-1,1]$.


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Additional Information

Alexandre Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: eremenko@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08640-0
PII: S 0002-9939(06)08640-0
Received by editor(s): September 1, 2005
Received by editor(s) in revised form: January 3, 2006
Published electronically: November 29, 2006
Additional Notes: The author was supported by NSF grants DMS-0100512 and DMS-0244421.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.