Abstract
Markov’s inequality is \[ sup [ − 1 , 1 ] | f ′ | ≤ ( deg f ) 2 sup [ − 1 , 1 ] | f | , \sup _{[-1,1]}|f’|\leq (\deg f)^2\sup _{[-1,1]}|f|, \] for all polynomials f f . We prove a precise version of this inequality with an arbitrary continuum in the complex plane instead of the interval [ − 1 , 1 ] [-1,1] .
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