Glasnik Matematicki, Vol. 32, No.2 (1997), 247-258.

Lp INEQUALITIES FOR POLYNOMIALS WITH RESTRICTED ZEROS

Abdul Aziz and W. M. Shah

Department of Mathematics and Statistics, University of Kashmir, Hazratbal Srinagar - 1900076, India

Abstract.   A theorem of De Bruijn concerning Lp inequalities for polynomials is extended to a class of lacunary type polynomials for every p > 0. Also a generalization of this result to the s-th derivative of polynomials not vanishing in the disk |z| < k where k >= 1 is obtained.

1991 Mathematics Subject Classification.   41A27.

Key words and phrases.   Polynomials, Lp mean estimates.

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