International Journal of Mathematics and Mathematical Sciences

Volume 16 (1993), Issue 2, Pages 289-296

doi:10.1155/S0161171293000341

## A generalization of an inequality of Zygmund

# R. Peretz

Department of Mathematics, University of Michigan, Ann Arbor 48109, MI, USA

Received 17 October 1990

Copyright © 1993 R. Peretz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The well known Bernstein Inequallty states that if

This is a consequence of a general equality that appears in Zygmund [7]
(and which is due to Bernstein and Szegö): For any polynomial

In this note we generalize the last result to domains different from
Euclidean disks by showing the following: If

We then obtain some conclusions for Schlicht Functions.