a generalization of an inequality of zygmund
Abstract
The well known Bernstein Inequallty states that if D is a disk
centered at the origin with radius R and if p(z) is a polynomial of
degree n, then maxz∈D|p′(z)|≤nRmaxz∈D|p(z)| with equality iff p(z)=AZn.
However it is true that we have the following better inequallty:
maxz∈D|p′(z)|≤nRmaxz∈D|Rep(z)|
with equality iff p(z)=AZn.
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243654
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10.1155/S0161171293000341
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