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A Markov-type inequality for arbitrary plane continua |
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| Authors: | Alexandre Eremenko |
| Affiliation: | Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 |
| Abstract: | Markov's inequality is ![$displaystyle sup_{[-1,1]}vert f'vertleq(deg f)^2sup_{[-1,1]}vert fvert,$](http://www.ams.org/proc/2007-135-05/S0002-9939-06-08640-0/gif-abstract0/img1.gif)  . We prove a precise version of this inequality with an arbitrary continuum in the complex plane instead of the interval ![$ [-1,1]$](http://www.ams.org/proc/2007-135-05/S0002-9939-06-08640-0/gif-abstract0/img3.gif){kind=small} . |
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