F( p + 3) - EMIS

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Euclidean disks by showing the following: If g(eix) is dtfferentlable and if p(z) Is a polynomial of degree n then for any s p< we have. Ig(el)p (g(ele))lPde. A n max.
Internat. J. Math. & Math. Sci. VOL. 16 NO. 2 (1993) 289-296

289

A GENERALIZATION OF AN INEQUALITY OF ZYGMUND R. PERETZ Department of Mathematlcs Unlverslty of Mlchlgan Ann Arbor, MI 48109

(Received October 17, 1990)

ABSTRACT.

The well known Bernsteln Inequallty states that If

D

Is a dlsk

centered at the origin wlth radlus R and If p(z) Is a polynomlal of dgree n, then max (z)l n max Ip(z)l wlth equallty iff p(z)

zD

IP’

Azn

zD

However It Is true that we have the followlng better inequallty:

Ip’Cz)l

max

zD

-