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A Markov-type inequality for arbitrary plane continua
Author(s):
Alexandre
Eremenko
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1505-1510.
MSC (2000):
Primary 41A17, 26D05
Posted:
November 29, 2006
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Abstract:
Markov's inequality is for all polynomials  . We prove a precise version of this inequality with an arbitrary continuum in the complex plane instead of the interval ![$ [-1,1]$](/proc/2007-135-05/S0002-9939-06-08640-0/gif-abstract0/img3.gif) .
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Additional Information:
Alexandre
Eremenko
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
eremenko@math.purdue.edu
DOI:
10.1090/S0002-9939-06-08640-0
PII:
S 0002-9939(06)08640-0
Received by editor(s):
September 1, 2005
Received by editor(s) in revised form:
January 3, 2006
Posted:
November 29, 2006
Additional Notes:
The author was supported by NSF grants DMS-0100512 and DMS-0244421.
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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![$\displaystyle \sup_{[-1,1]}\vert f'\vert\leq(\deg f)^2\sup_{[-1,1]}\vert f\vert,$](/proc/2007-135-05/S0002-9939-06-08640-0/gif-abstract0/img1.gif)
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